Pub Date : 2020-12-09DOI: 10.1103/PhysRevResearch.3.023118
Amos Chan, A. De Luca, J. Chalker
We consider the spectral statistics of the Floquet operator for disordered, periodically driven spin chains in their quantum chaotic and many-body localized phases (MBL). The spectral statistics are characterized by the traces of powers $t$ of the Floquet operator, and our approach hinges on the fact that, for integer $t$ in systems with local interactions, these traces can be re-expressed in terms of products of dual transfer matrices, each representing a spatial slice of the system. We focus on properties of the dual transfer matrix products as represented by a spectrum of Lyapunov exponents, which we call textit{spectral Lyapunov exponents}. In particular, we examine the features of this spectrum that distinguish chaotic and MBL phases. The transfer matrices can be block-diagonalized using time-translation symmetry, and so the spectral Lyapunov exponents are classified according to a momentum in the time direction. For large $t$ we argue that the leading Lyapunov exponents in each momentum sector tend to zero in the chaotic phase, while they remain finite in the MBL phase. These conclusions are based on results from three complementary types of calculation. We find exact results for the chaotic phase by considering a Floquet random quantum circuit with on-site Hilbert space dimension $q$ in the large-$q$ limit. In the MBL phase, we show that the spectral Lyapunov exponents remain finite by systematically analyzing models of non-interacting systems, weakly coupled systems, and local integrals of motion. Numerically, we compute the Lyapunov exponents for a Floquet random quantum circuit and for the kicked Ising model in the two phases. As an additional result, we calculate exactly the higher point spectral form factors (hpSFF) in the large-$q$ limit, and show that the generalized Thouless time scales logarithmically in system size for all hpSFF in the large-$q$ chaotic phase.
{"title":"Spectral Lyapunov exponents in chaotic and localized many-body quantum systems","authors":"Amos Chan, A. De Luca, J. Chalker","doi":"10.1103/PhysRevResearch.3.023118","DOIUrl":"https://doi.org/10.1103/PhysRevResearch.3.023118","url":null,"abstract":"We consider the spectral statistics of the Floquet operator for disordered, periodically driven spin chains in their quantum chaotic and many-body localized phases (MBL). The spectral statistics are characterized by the traces of powers $t$ of the Floquet operator, and our approach hinges on the fact that, for integer $t$ in systems with local interactions, these traces can be re-expressed in terms of products of dual transfer matrices, each representing a spatial slice of the system. We focus on properties of the dual transfer matrix products as represented by a spectrum of Lyapunov exponents, which we call textit{spectral Lyapunov exponents}. In particular, we examine the features of this spectrum that distinguish chaotic and MBL phases. The transfer matrices can be block-diagonalized using time-translation symmetry, and so the spectral Lyapunov exponents are classified according to a momentum in the time direction. For large $t$ we argue that the leading Lyapunov exponents in each momentum sector tend to zero in the chaotic phase, while they remain finite in the MBL phase. These conclusions are based on results from three complementary types of calculation. We find exact results for the chaotic phase by considering a Floquet random quantum circuit with on-site Hilbert space dimension $q$ in the large-$q$ limit. In the MBL phase, we show that the spectral Lyapunov exponents remain finite by systematically analyzing models of non-interacting systems, weakly coupled systems, and local integrals of motion. Numerically, we compute the Lyapunov exponents for a Floquet random quantum circuit and for the kicked Ising model in the two phases. As an additional result, we calculate exactly the higher point spectral form factors (hpSFF) in the large-$q$ limit, and show that the generalized Thouless time scales logarithmically in system size for all hpSFF in the large-$q$ chaotic phase.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80693461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-03DOI: 10.21468/SCIPOSTPHYS.10.3.070
O. Gamayun, N. Iorgov, Y. Zhuravlev
We introduce effective form factors for one-dimensional lattice fermions with arbitrary phase shifts. We study tau functions defined as series of these form factors. On the one hand we perform the exact summation and present tau functions as Fredholm determinants in the thermodynamic limit. On the other hand simple expressions of form factors allow us to present the corresponding series as integrals of elementary functions. Using this approach we re-derive the asymptotics of static correlation functions of the XY quantum chain at finite temperature.
{"title":"Effective free-fermionic form factors and the XY spin chain","authors":"O. Gamayun, N. Iorgov, Y. Zhuravlev","doi":"10.21468/SCIPOSTPHYS.10.3.070","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYS.10.3.070","url":null,"abstract":"We introduce effective form factors for one-dimensional lattice fermions with arbitrary phase shifts. We study tau functions defined as series of these form factors. On the one hand we perform the exact summation and present tau functions as Fredholm determinants in the thermodynamic limit. On the other hand simple expressions of form factors allow us to present the corresponding series as integrals of elementary functions. Using this approach we re-derive the asymptotics of static correlation functions of the XY quantum chain at finite temperature.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76406360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-02DOI: 10.1103/PhysRevB.103.224304
S. Bhattacharjee, Souvik Bandyopadhyay, D. Sen, A. Dutta
We present a complete topological characterization of a bilayer composite of two Chern insulators (specifically, Haldane models) and explicitly establish the bulk-boundary correspondences. We show that the non-Abelian Chern number (NACN) accurately maps out all the possible phases of the system as it remains well-defined even in the presence of degeneracies in the occupied bands. Importantly, our result paves the way for realizing adiabatic preparation of monolayer Chern insulators. This has been a major challenge till date, given the impossibility of unitarily connecting inequivalent topological phases. We show that this difficulty can be circumvented by adiabatically varying the interlayer coupling in such a way that the system remains gapped at all times. In particular, a complete knowledge of the phase diagram of the bilayer composite immediately allows one to identify all such adiabatic passages which can be traversed to tune the phases of the individual monolayers.
{"title":"Bilayer Haldane system: Topological characterization and adiabatic passages connecting Chern phases","authors":"S. Bhattacharjee, Souvik Bandyopadhyay, D. Sen, A. Dutta","doi":"10.1103/PhysRevB.103.224304","DOIUrl":"https://doi.org/10.1103/PhysRevB.103.224304","url":null,"abstract":"We present a complete topological characterization of a bilayer composite of two Chern insulators (specifically, Haldane models) and explicitly establish the bulk-boundary correspondences. We show that the non-Abelian Chern number (NACN) accurately maps out all the possible phases of the system as it remains well-defined even in the presence of degeneracies in the occupied bands. Importantly, our result paves the way for realizing adiabatic preparation of monolayer Chern insulators. This has been a major challenge till date, given the impossibility of unitarily connecting inequivalent topological phases. We show that this difficulty can be circumvented by adiabatically varying the interlayer coupling in such a way that the system remains gapped at all times. In particular, a complete knowledge of the phase diagram of the bilayer composite immediately allows one to identify all such adiabatic passages which can be traversed to tune the phases of the individual monolayers.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"22 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91425565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.21468/SciPostPhys.10.6.134
A. Chlebicki, P. Jakubczyk
We employ the functional renormalization group framework at second order in the derivative expansion to study the $O(N)$ models continuously varying the number of field components $N$ and the spatial dimensionality $d$. Of our special interest are phenomena occurring in the vicinity of $d=2$. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents $nu$ and $eta$ across a line in the $(d,N)$ plane, which passes through the point $(2,2)$. By direct numerical evaluation of $eta(d,N)$ and $nu^{-1}(d,N)$ we find no evidence of discontinuous or singular first and second derivatives of these functions for $d>2$. The computed derivatives of $eta(d,N)$ and $nu^{-1}(d,N)$ become increasingly large for $dto 2$ and $Nto 2$ and it is only in this limit that $eta(d,N)$ and $nu^{-1}(d,N)$ as obtained by us are evidently nonanalytical. The derivatives of the exponents show, nonetheless, a locus of maxima located along a line in the $(d,N)$-plane, with magnitude controlled by the distance from the point $(d,N)=(2,2)$. This locus is situated close to the expected position of the Cardy-Hamber nonanalyticity line. We provide a discussion of the evolution of the obtained picture upon varying $d$ and $N$ between $(d,N)=(2,2)$ and other, earlier studied cases, such as $dto 3$ or $Nto infty$.
{"title":"Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization","authors":"A. Chlebicki, P. Jakubczyk","doi":"10.21468/SciPostPhys.10.6.134","DOIUrl":"https://doi.org/10.21468/SciPostPhys.10.6.134","url":null,"abstract":"We employ the functional renormalization group framework at second order in the derivative expansion to study the $O(N)$ models continuously varying the number of field components $N$ and the spatial dimensionality $d$. Of our special interest are phenomena occurring in the vicinity of $d=2$. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents $nu$ and $eta$ across a line in the $(d,N)$ plane, which passes through the point $(2,2)$. By direct numerical evaluation of $eta(d,N)$ and $nu^{-1}(d,N)$ we find no evidence of discontinuous or singular first and second derivatives of these functions for $d>2$. The computed derivatives of $eta(d,N)$ and $nu^{-1}(d,N)$ become increasingly large for $dto 2$ and $Nto 2$ and it is only in this limit that $eta(d,N)$ and $nu^{-1}(d,N)$ as obtained by us are evidently nonanalytical. The derivatives of the exponents show, nonetheless, a locus of maxima located along a line in the $(d,N)$-plane, with magnitude controlled by the distance from the point $(d,N)=(2,2)$. This locus is situated close to the expected position of the Cardy-Hamber nonanalyticity line. We provide a discussion of the evolution of the obtained picture upon varying $d$ and $N$ between $(d,N)=(2,2)$ and other, earlier studied cases, such as $dto 3$ or $Nto infty$.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89409218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-30DOI: 10.1103/PHYSREVB.103.104305
Lorenzo Monacelli, F. Mauri
Most material properties of great physical interest are directly related to nuclear dynamics, e.g. the ionic thermal conductivity, Raman/IR vibrational spectra, inelastic X-ray, and Neutron scattering. A theory able to compute from first principles these properties, fully accounting for the quantum nature of the nuclei and the anharmonicity in the nuclear energy landscape that can be implemented in systems with hundreds of atoms is missing. Here, we derive an approximated theory for the quantum time evolution of lattice vibrations at finite temperature. This theory introduces the time dynamics in the Self-Consistent Harmonic Approximation (SCHA) and shares with the static case the same computational cost. It is nonempirical, as pure states evolve according to the Dirac least action principle and the dynamics of the thermal ensemble conserves both energy and entropy. The static SCHA is recovered as a stationary solution of the dynamical equations. We apply perturbation theory around the static SCHA solution and derive an algorithm to compute efficiently quantum dynamical correlation functions. Thanks to this new algorithm, we have access to the response function of any general external time-dependent perturbation, enabling the simulation of phonon spectra without following any perturbative expansion of the nuclear potential or empirical methods. We benchmark the method on the IR and Raman spectroscopy of high-pressure hydrogen phase III, with a simulation cell of 96 atoms. Our work also explores the nonlinear regime of the dynamical nuclear motion, providing a paradigm to simulate the interaction with intense or multiple probes, as in pump-probe spectroscopy, or chemical reactions involving light atoms, as the proton transfer in biomolecules.
{"title":"Time-dependent self-consistent harmonic approximation: Anharmonic nuclear quantum dynamics and time correlation functions","authors":"Lorenzo Monacelli, F. Mauri","doi":"10.1103/PHYSREVB.103.104305","DOIUrl":"https://doi.org/10.1103/PHYSREVB.103.104305","url":null,"abstract":"Most material properties of great physical interest are directly related to nuclear dynamics, e.g. the ionic thermal conductivity, Raman/IR vibrational spectra, inelastic X-ray, and Neutron scattering. A theory able to compute from first principles these properties, fully accounting for the quantum nature of the nuclei and the anharmonicity in the nuclear energy landscape that can be implemented in systems with hundreds of atoms is missing. Here, we derive an approximated theory for the quantum time evolution of lattice vibrations at finite temperature. This theory introduces the time dynamics in the Self-Consistent Harmonic Approximation (SCHA) and shares with the static case the same computational cost. It is nonempirical, as pure states evolve according to the Dirac least action principle and the dynamics of the thermal ensemble conserves both energy and entropy. The static SCHA is recovered as a stationary solution of the dynamical equations. We apply perturbation theory around the static SCHA solution and derive an algorithm to compute efficiently quantum dynamical correlation functions. Thanks to this new algorithm, we have access to the response function of any general external time-dependent perturbation, enabling the simulation of phonon spectra without following any perturbative expansion of the nuclear potential or empirical methods. We benchmark the method on the IR and Raman spectroscopy of high-pressure hydrogen phase III, with a simulation cell of 96 atoms. Our work also explores the nonlinear regime of the dynamical nuclear motion, providing a paradigm to simulate the interaction with intense or multiple probes, as in pump-probe spectroscopy, or chemical reactions involving light atoms, as the proton transfer in biomolecules.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89745970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-19DOI: 10.1103/PHYSREVB.103.094303
J. Feldmeier, F. Pollmann, M. Knap
We study the late time relaxation dynamics of a pure $U(1)$ lattice gauge theory in the form of a dimer model on a bilayer geometry. To this end, we first develop a proper notion of hydrodynamic transport in such a system by constructing a global conservation law that can be attributed to the presence of topological solitons. The correlation functions of local objects charged under this conservation law can then be used to study the universal properties of the dynamics at late times, applicable to both quantum and classical systems. Performing the time evolution via classically simulable automata circuits unveils a rich phenomenology of the system's non-equilibrium properties: For a large class of relevant initial states, local charges are effectively restricted to move along one-dimensional 'tubes' within the quasi-two-dimensional system, displaying fracton-like mobility constraints. The time scale on which these tubes are stable diverges with increasing systems size, yielding a novel mechanism for non-ergodic behavior in the thermodynamic limit. We further explore the role of geometry by studying the system in a quasi-one-dimensional limit, where the Hilbert space is strongly fragmented due to the emergence of an extensive number of conserved quantities. This provides an instance of a recently introduced concept of 'statistically localized integrals of motion', whose universal anomalous hydrodynamics we determine by a mapping to a problem of classical tracer diffusion. We conclude by discussing how our approach might generalize to study transport in other lattice gauge theories.
{"title":"Emergent fracton dynamics in a nonplanar dimer model","authors":"J. Feldmeier, F. Pollmann, M. Knap","doi":"10.1103/PHYSREVB.103.094303","DOIUrl":"https://doi.org/10.1103/PHYSREVB.103.094303","url":null,"abstract":"We study the late time relaxation dynamics of a pure $U(1)$ lattice gauge theory in the form of a dimer model on a bilayer geometry. To this end, we first develop a proper notion of hydrodynamic transport in such a system by constructing a global conservation law that can be attributed to the presence of topological solitons. The correlation functions of local objects charged under this conservation law can then be used to study the universal properties of the dynamics at late times, applicable to both quantum and classical systems. Performing the time evolution via classically simulable automata circuits unveils a rich phenomenology of the system's non-equilibrium properties: For a large class of relevant initial states, local charges are effectively restricted to move along one-dimensional 'tubes' within the quasi-two-dimensional system, displaying fracton-like mobility constraints. The time scale on which these tubes are stable diverges with increasing systems size, yielding a novel mechanism for non-ergodic behavior in the thermodynamic limit. We further explore the role of geometry by studying the system in a quasi-one-dimensional limit, where the Hilbert space is strongly fragmented due to the emergence of an extensive number of conserved quantities. This provides an instance of a recently introduced concept of 'statistically localized integrals of motion', whose universal anomalous hydrodynamics we determine by a mapping to a problem of classical tracer diffusion. We conclude by discussing how our approach might generalize to study transport in other lattice gauge theories.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82051550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-16DOI: 10.1103/PHYSREVRESEARCH.3.L012023
Asaf Miron, S. Reuveni
Stochastic resetting models diverse phenomena across numerous scientific disciplines. Current understanding stems from the renewal framework, which relates systems subject to global resetting to their non-resetting counterparts. Yet, in interacting many-body systems, even the simplest scenarios involving resetting give rise to the notion of local resetting, whose analysis falls outside the scope of the renewal approach. A prime example is that of diffusing particles with excluded volume interactions that independently attempt to reset their position to the origin of a 1D lattice. With renewal rendered ineffective, we instead employ a mean-field approach whose validity is corroborated via extensive numerical simulations. The emerging picture sheds first light on the non-trivial interplay between interactions and resetting in many-body systems.
{"title":"Diffusion with local resetting and exclusion","authors":"Asaf Miron, S. Reuveni","doi":"10.1103/PHYSREVRESEARCH.3.L012023","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.3.L012023","url":null,"abstract":"Stochastic resetting models diverse phenomena across numerous scientific disciplines. Current understanding stems from the renewal framework, which relates systems subject to global resetting to their non-resetting counterparts. Yet, in interacting many-body systems, even the simplest scenarios involving resetting give rise to the notion of local resetting, whose analysis falls outside the scope of the renewal approach. A prime example is that of diffusing particles with excluded volume interactions that independently attempt to reset their position to the origin of a 1D lattice. With renewal rendered ineffective, we instead employ a mean-field approach whose validity is corroborated via extensive numerical simulations. The emerging picture sheds first light on the non-trivial interplay between interactions and resetting in many-body systems.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75056941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-16DOI: 10.1103/PHYSREVB.103.104302
F. Surace, Matteo Votto, Eduardo Gonzalez Lazo, Alessandro Silva, M. Dalmonte, G. Giudici
Quantum scars are non-thermal eigenstates characterized by low entanglement entropy, initially detected in systems subject to nearest-neighbor Rydberg blockade, the so called PXP model. While most of these special eigenstates elude an analytical description and seem to hybridize with nearby thermal eigenstates for large systems, some of them can be written as matrix product states (MPS) with size-independent bond dimension. We study the response of these exact quantum scars to perturbations by analysing the scaling of the fidelity susceptibility with system size. We find that some of them are anomalously stable at first order in perturbation theory, in sharp contrast to the eigenstate thermalization hypothesis. However, this stability seems to breakdown when all orders are taken into account. We further investigate models with larger blockade radius and find a novel set of exact quantum scars, that we write down analytically and compare with the PXP exact eigenstates. We show that they exhibit the same robustness against perturbations at first order.
{"title":"Exact many-body scars and their stability in constrained quantum chains","authors":"F. Surace, Matteo Votto, Eduardo Gonzalez Lazo, Alessandro Silva, M. Dalmonte, G. Giudici","doi":"10.1103/PHYSREVB.103.104302","DOIUrl":"https://doi.org/10.1103/PHYSREVB.103.104302","url":null,"abstract":"Quantum scars are non-thermal eigenstates characterized by low entanglement entropy, initially detected in systems subject to nearest-neighbor Rydberg blockade, the so called PXP model. While most of these special eigenstates elude an analytical description and seem to hybridize with nearby thermal eigenstates for large systems, some of them can be written as matrix product states (MPS) with size-independent bond dimension. We study the response of these exact quantum scars to perturbations by analysing the scaling of the fidelity susceptibility with system size. We find that some of them are anomalously stable at first order in perturbation theory, in sharp contrast to the eigenstate thermalization hypothesis. However, this stability seems to breakdown when all orders are taken into account. We further investigate models with larger blockade radius and find a novel set of exact quantum scars, that we write down analytically and compare with the PXP exact eigenstates. We show that they exhibit the same robustness against perturbations at first order.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86687516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-14DOI: 10.1103/PhysRevB.103.L201108
X. Zotos
The time evolution of local operators in quantum compass models is characterized by simplicity as it can be represented as expanding and contracting strings of operators. Here we present an analytical solution to the problem of growth of a local energy operator in a quantum compass model on a Bethe lattice. We find a linear increase in time of the average operator length and a diffusive spreading of the operator length distribution. By a moment method we evaluate the local energy autocorrelation function that shows a Lorentzian shape at low frequencies. Furthermore, by a stochastic method we visualize the expansion of the string cloud.
{"title":"Operator growth in a quantum compass model on a Bethe lattice","authors":"X. Zotos","doi":"10.1103/PhysRevB.103.L201108","DOIUrl":"https://doi.org/10.1103/PhysRevB.103.L201108","url":null,"abstract":"The time evolution of local operators in quantum compass models is characterized by simplicity as it can be represented as expanding and contracting strings of operators. Here we present an analytical solution to the problem of growth of a local energy operator in a quantum compass model on a Bethe lattice. We find a linear increase in time of the average operator length and a diffusive spreading of the operator length distribution. By a moment method we evaluate the local energy autocorrelation function that shows a Lorentzian shape at low frequencies. Furthermore, by a stochastic method we visualize the expansion of the string cloud.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87969084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-12DOI: 10.1103/PHYSREVB.103.115132
Lucas Sá, P. Ribeiro, T. Prosen
We explicitly construct an integrable interacting dissipative quantum circuit, via a trotterization of the Hubbard model with imaginary interaction strength. To prove integrability, we build an inhomogeneous transfer matrix, from which conserved super-operator charges can be derived, in particular, the circuit's dynamical generator. After showing the trace preservation and complete positivity of local maps, we reinterpret them as the Kraus representation of the dynamics of free fermions with single-site dephasing. The integrability of the map is broken by adding interactions to the local coherent dynamics or by removing the dephasing. Moreover, the construction allows us to explicitly build circuits belonging to different non-Hermitian symmetry classes, which are characterized by the behavior under transposition instead of complex conjugation. We confirm all our analytical results by using complex spacing ratios to examine the spectral statistics of the dissipative circuits.
{"title":"Integrable nonunitary open quantum circuits","authors":"Lucas Sá, P. Ribeiro, T. Prosen","doi":"10.1103/PHYSREVB.103.115132","DOIUrl":"https://doi.org/10.1103/PHYSREVB.103.115132","url":null,"abstract":"We explicitly construct an integrable interacting dissipative quantum circuit, via a trotterization of the Hubbard model with imaginary interaction strength. To prove integrability, we build an inhomogeneous transfer matrix, from which conserved super-operator charges can be derived, in particular, the circuit's dynamical generator. After showing the trace preservation and complete positivity of local maps, we reinterpret them as the Kraus representation of the dynamics of free fermions with single-site dephasing. The integrability of the map is broken by adding interactions to the local coherent dynamics or by removing the dephasing. Moreover, the construction allows us to explicitly build circuits belonging to different non-Hermitian symmetry classes, which are characterized by the behavior under transposition instead of complex conjugation. We confirm all our analytical results by using complex spacing ratios to examine the spectral statistics of the dissipative circuits.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"291 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76880969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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