Pub Date : 2020-06-14DOI: 10.21468/SCIPOSTPHYS.9.5.063
A. Shapira, KAY Joerg WIESE
We give a simplified proof for the equivalence of loop-erased random walks to a lattice model containing two complex fermions, and one complex boson. This equivalence works on an arbitrary directed graph. Specifying to the $d$-dimensional hypercubic lattice, at large scales this theory reduces to a scalar $phi^4$-type theory with two complex fermions, and one complex boson. While the path integral for the fermions is the Berezin integral, for the bosonic field we can either use a complex field $phi(x)in mathbb C$ (standard formulation) or a nilpotent one satisfying $phi(x)^2 =0$. We discuss basic properties of the latter formulation, which has distinct advantages in the lattice model.
{"title":"An exact mapping between loop-erased random walks and an interacting field theory with two fermions and one boson","authors":"A. Shapira, KAY Joerg WIESE","doi":"10.21468/SCIPOSTPHYS.9.5.063","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYS.9.5.063","url":null,"abstract":"We give a simplified proof for the equivalence of loop-erased random walks to a lattice model containing two complex fermions, and one complex boson. This equivalence works on an arbitrary directed graph. Specifying to the $d$-dimensional hypercubic lattice, at large scales this theory reduces to a scalar $phi^4$-type theory with two complex fermions, and one complex boson. While the path integral for the fermions is the Berezin integral, for the bosonic field we can either use a complex field $phi(x)in mathbb C$ (standard formulation) or a nilpotent one satisfying $phi(x)^2 =0$. We discuss basic properties of the latter formulation, which has distinct advantages in the lattice model.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73414580","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 : 2020-06-12DOI: 10.1103/PHYSREVX.11.011022
Pavel Kos, B. Bertini, T. Prosen
Interacting many-body systems with explicitly accessible spatio-temporal correlation functions are extremely rare, especially in the absence of integrability. Recently, we identified a remarkable class of such systems and termed them dual-unitary quantum circuits. These are brick-wall type local quantum circuits whose dynamics are unitary in both time and space. For these systems the spatio-temporal correlation functions are non-trivial only at the edge of the causal light cone and can be computed in terms of one-dimensional transfer matrices. Dual-unitarity, however, requires fine-tuning and the degree of generality of the observed dynamical features remained unclear. Here we address this question by introducing perturbations. First we show that if the deviation from dual-unitarity is random and independently distributed at each space-time point, dynamical correlations maintain the dual-unitary form. Then, considering fixed perturbations, we prove that for a particular class of unperturbed elementary dual-unitary gates the correlation functions are still expressed in terms of one-dimensional transfer matrices. These matrices, however, are now contracted over generic paths connecting the origin to a fixed end point inside the causal light cone. The correlation function is given as a sum over all such paths. Our statement is rigours in the "dilute limit", where only a small fraction of the gates is perturbed, and in the presence of random longitudinal fields, but we provide theoretical arguments and stringent numerical checks supporting its validity even in the clean case and when all gates are perturbed. As a byproduct, in the case of random longitudinal fields -- which turns out to be equivalent to classical Markov circuits -- we find four types of non-dual-unitary interacting many-body systems where the correlation functions are exactly given by the path-sum formula.
{"title":"Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula","authors":"Pavel Kos, B. Bertini, T. Prosen","doi":"10.1103/PHYSREVX.11.011022","DOIUrl":"https://doi.org/10.1103/PHYSREVX.11.011022","url":null,"abstract":"Interacting many-body systems with explicitly accessible spatio-temporal correlation functions are extremely rare, especially in the absence of integrability. Recently, we identified a remarkable class of such systems and termed them dual-unitary quantum circuits. These are brick-wall type local quantum circuits whose dynamics are unitary in both time and space. For these systems the spatio-temporal correlation functions are non-trivial only at the edge of the causal light cone and can be computed in terms of one-dimensional transfer matrices. Dual-unitarity, however, requires fine-tuning and the degree of generality of the observed dynamical features remained unclear. Here we address this question by introducing perturbations. First we show that if the deviation from dual-unitarity is random and independently distributed at each space-time point, dynamical correlations maintain the dual-unitary form. Then, considering fixed perturbations, we prove that for a particular class of unperturbed elementary dual-unitary gates the correlation functions are still expressed in terms of one-dimensional transfer matrices. These matrices, however, are now contracted over generic paths connecting the origin to a fixed end point inside the causal light cone. The correlation function is given as a sum over all such paths. Our statement is rigours in the \"dilute limit\", where only a small fraction of the gates is perturbed, and in the presence of random longitudinal fields, but we provide theoretical arguments and stringent numerical checks supporting its validity even in the clean case and when all gates are perturbed. As a byproduct, in the case of random longitudinal fields -- which turns out to be equivalent to classical Markov circuits -- we find four types of non-dual-unitary interacting many-body systems where the correlation functions are exactly given by the path-sum formula.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77246270","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}
Joren Vanherck, C. Bacaksiz, B. Sor'ee, M. Milošević, W. Magnus
Recent years have seen a tremendous rise of two-dimensional (2D) magnetic materials, several of which verified experimentally. However, most of the theoretical predictions to date rely on ab-initio methods, at zero temperature and fluctuations-free, while one certainly expects detrimental quantum fluctuations at finite temperatures. Here we present the solution of the quantum Heisenberg model for honeycomb/hexagonal lattices with anisotropic exchange interaction up to third nearest neighbors and in an applied field in arbitrary direction, that answers the question whether long-range magnetization can indeed survive in the ultrathin limit of materials, up to which temperature, and what the characteristic excitation (magnon) frequencies are, all essential to envisaged applications of magnetic 2D materials. We validate the calculations on the examples of monolayer CrI3, CrBr3 and MnSe2. Moreover, we provide an easy-to-use tool to calculate Curie temperatures of new 2D computational materials.
{"title":"2D ferromagnetism at finite temperatures under quantum scrutiny","authors":"Joren Vanherck, C. Bacaksiz, B. Sor'ee, M. Milošević, W. Magnus","doi":"10.1063/5.0015619","DOIUrl":"https://doi.org/10.1063/5.0015619","url":null,"abstract":"Recent years have seen a tremendous rise of two-dimensional (2D) magnetic materials, several of which verified experimentally. However, most of the theoretical predictions to date rely on ab-initio methods, at zero temperature and fluctuations-free, while one certainly expects detrimental quantum fluctuations at finite temperatures. Here we present the solution of the quantum Heisenberg model for honeycomb/hexagonal lattices with anisotropic exchange interaction up to third nearest neighbors and in an applied field in arbitrary direction, that answers the question whether long-range magnetization can indeed survive in the ultrathin limit of materials, up to which temperature, and what the characteristic excitation (magnon) frequencies are, all essential to envisaged applications of magnetic 2D materials. We validate the calculations on the examples of monolayer CrI3, CrBr3 and MnSe2. Moreover, we provide an easy-to-use tool to calculate Curie temperatures of new 2D computational materials.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78809202","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 : 2020-06-02DOI: 10.1103/physrevresearch.2.033423
Sudip Mukherjee, A. Basu
We revisit the effects of short-ranged random quenched disorder on the universal scaling properties of the classical $N$-vector model with cubic anisotropy. We set up the nonconserved relaxational dynamics of the model, and study the universal dynamic scaling near the second order phase transition. We extract the critical exponents and the dynamic exponent in a one-loop dynamic renormalisation group calculation with short-ranged isotropic disorder. We show that the dynamics near a critical point is generically slower when the quenched disorder is relevant than when it is not, independent of whether the pure model is isotropic or cubic anisotropic. We demonstrate the surprising thresholdless instability of the associated universality class due to perturbations from rotational invariance breaking quenched disorder-order parameter coupling, indicating breakdown of dynamic scaling. We speculate that this may imply a novel first order transition in the model, induced by a symmetry-breaking disorder.
{"title":"Dynamic scaling in the quenched disordered classicalN-vector model","authors":"Sudip Mukherjee, A. Basu","doi":"10.1103/physrevresearch.2.033423","DOIUrl":"https://doi.org/10.1103/physrevresearch.2.033423","url":null,"abstract":"We revisit the effects of short-ranged random quenched disorder on the universal scaling properties of the classical $N$-vector model with cubic anisotropy. We set up the nonconserved relaxational dynamics of the model, and study the universal dynamic scaling near the second order phase transition. We extract the critical exponents and the dynamic exponent in a one-loop dynamic renormalisation group calculation with short-ranged isotropic disorder. We show that the dynamics near a critical point is generically slower when the quenched disorder is relevant than when it is not, independent of whether the pure model is isotropic or cubic anisotropic. We demonstrate the surprising thresholdless instability of the associated universality class due to perturbations from rotational invariance breaking quenched disorder-order parameter coupling, indicating breakdown of dynamic scaling. We speculate that this may imply a novel first order transition in the model, induced by a symmetry-breaking disorder.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78124358","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}
We look into the Mpemba effect---the initially hotter sample cools sooner---in a molecular gas with nonlinear viscous drag. Specifically, the gas particles interact among them via elastic collisions and also with a background fluid at equilibrium. Thus, within the framework of kinetic theory, our gas is described by an Enskog--Fokker--Planck equation. The analysis is carried out in the first Sonine approximation, in which the evolution of the temperature is coupled to that of the excess kurtosis. This coupling leads to the emergence of the Mpemba effect, which is observed in an early stage of the relaxation and when the initial temperatures of the two samples are close enough. This allows for the development of a simple theory, linearizing the temperature evolution around a reference temperature---namely the initial temperature closer to the asymptotic equilibrium value. The linear theory provides a semiquantitative description of the effect, including expressions for the crossover time and the maximum temperature difference. We also discuss the limitations of our linearized theory.
{"title":"Mpemba effect in molecular gases under nonlinear drag","authors":"Andrés Santos, A. Prados","doi":"10.1063/5.0016243","DOIUrl":"https://doi.org/10.1063/5.0016243","url":null,"abstract":"We look into the Mpemba effect---the initially hotter sample cools sooner---in a molecular gas with nonlinear viscous drag. Specifically, the gas particles interact among them via elastic collisions and also with a background fluid at equilibrium. Thus, within the framework of kinetic theory, our gas is described by an Enskog--Fokker--Planck equation. The analysis is carried out in the first Sonine approximation, in which the evolution of the temperature is coupled to that of the excess kurtosis. This coupling leads to the emergence of the Mpemba effect, which is observed in an early stage of the relaxation and when the initial temperatures of the two samples are close enough. This allows for the development of a simple theory, linearizing the temperature evolution around a reference temperature---namely the initial temperature closer to the asymptotic equilibrium value. The linear theory provides a semiquantitative description of the effect, including expressions for the crossover time and the maximum temperature difference. We also discuss the limitations of our linearized theory.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73140052","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 : 2020-06-01DOI: 10.1103/PHYSREVRESEARCH.2.043036
A. Kosior, M. Heyl
Entanglement has become central for the characterization of quantum matter both in and out of equilibrium. In a dynamical context entanglement exhibits universal linear temporal growth in generic systems, which stems from the underlying linear light cones as they occur in planar geometries. Inhomogeneous spacetimes can lead, however, to strongly bent trajectories. While such bent trajectories crucially impact correlation spreading and therefore the light-cone structure, it has remained elusive how this influences the entanglement dynamics. In this work we investigate the real-time evolution of the entanglement entropy in one-dimensional quantum systems after quenches which change the underlying spacetime background of the Hamiltonian. Concretely, we focus on the Rindler space describing the spacetime in close vicinity to a black hole. As a main result we find that entanglement grows sublinearly in a generic fashion both for interacting and noninteracting quantum matter. We further observe that the asymptotic relaxation becomes exponential, as opposed to algebraic for planar Minkowski spacetimes, and that in the vicinity of the black hole the relaxation time for large subsystems becomes independent of the subsystem size. We study entanglement dynamics both for the case of noninteracting fermions, allowing for exact numerical solutions, and for random unitary circuits representing a paradigmatic class of ergodic systems.
{"title":"Nonlinear entanglement growth in inhomogeneous space-times","authors":"A. Kosior, M. Heyl","doi":"10.1103/PHYSREVRESEARCH.2.043036","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.2.043036","url":null,"abstract":"Entanglement has become central for the characterization of quantum matter both in and out of equilibrium. In a dynamical context entanglement exhibits universal linear temporal growth in generic systems, which stems from the underlying linear light cones as they occur in planar geometries. Inhomogeneous spacetimes can lead, however, to strongly bent trajectories. While such bent trajectories crucially impact correlation spreading and therefore the light-cone structure, it has remained elusive how this influences the entanglement dynamics. In this work we investigate the real-time evolution of the entanglement entropy in one-dimensional quantum systems after quenches which change the underlying spacetime background of the Hamiltonian. Concretely, we focus on the Rindler space describing the spacetime in close vicinity to a black hole. As a main result we find that entanglement grows sublinearly in a generic fashion both for interacting and noninteracting quantum matter. We further observe that the asymptotic relaxation becomes exponential, as opposed to algebraic for planar Minkowski spacetimes, and that in the vicinity of the black hole the relaxation time for large subsystems becomes independent of the subsystem size. We study entanglement dynamics both for the case of noninteracting fermions, allowing for exact numerical solutions, and for random unitary circuits representing a paradigmatic class of ergodic systems.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78072955","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 : 2020-05-29DOI: 10.1103/PHYSREVRESEARCH.3.013075
Benjamin Walter, G. Pruessner, G. Salbreux
We introduce a perturbative method to calculate all moments of the first-passage time distribution in stochastic one-dimensional processes which are subject to both white and coloured noise. This class of non-Markovian processes is at the centre of the study of thermal active matter, that is self-propelled particles subject to diffusion. The perturbation theory about the Markov process considers the effect of self-propulsion to be small compared to that of thermal fluctuations. To illustrate our method, we apply it to the case of active thermal particles (i) in a harmonic trap (ii) on a ring. For both we calculate the first-order correction of the moment-generating function of first-passage times, and thus to all its moments. Our analytical results are compared to numerics.
{"title":"First passage time distribution of active thermal particles in potentials","authors":"Benjamin Walter, G. Pruessner, G. Salbreux","doi":"10.1103/PHYSREVRESEARCH.3.013075","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.3.013075","url":null,"abstract":"We introduce a perturbative method to calculate all moments of the first-passage time distribution in stochastic one-dimensional processes which are subject to both white and coloured noise. This class of non-Markovian processes is at the centre of the study of thermal active matter, that is self-propelled particles subject to diffusion. The perturbation theory about the Markov process considers the effect of self-propulsion to be small compared to that of thermal fluctuations. To illustrate our method, we apply it to the case of active thermal particles (i) in a harmonic trap (ii) on a ring. For both we calculate the first-order correction of the moment-generating function of first-passage times, and thus to all its moments. Our analytical results are compared to numerics.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81768447","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}
Non-Newtonian transport properties of an inertial suspension of inelastic rough hard spheres under simple shear flow are determined from the Boltzmann kinetic equation. The influence of the interstitial gas on rough hard spheres is modeled via a Fokker-Planck generalized equation for rotating spheres accounting for the coupling of both the translational and rotational degrees of freedom of grains with the background viscous gas. The generalized Fokker-Planck term is the sum of two ordinary Fokker-Planck differential operators in linear $mathbf{v}$ and angular $boldsymbol{omega}$ velocity space. As usual, each Fokker-Planck operator is constituted by a drag force term (proportional to $mathbf{v}$ and/or $boldsymbol{omega}$) plus a stochastic Langevin term defined in terms of the background temperature $T_text{ex}$. The Boltzmann equation is solved by two different but complementary approaches: (i) by means of Grad's moment method, and (ii) by using a Bhatnagar-Gross-Krook (BGK)-type kinetic model adapted to inelastic rough hard spheres. As occurs in the case of emph{smooth} inelastic hard spheres, our results show that both the temperature and the non-Newtonian viscosity increase drastically with increasing the shear rate (discontinuous shear thickening effect) while the fourth-degree velocity moments also exhibit an $S$-shape. In particular, while high levels of roughness may slightly attenuate the jump of the viscosity in comparison to the smooth case, the opposite happens for the rotational temperature. As an application of these results, a linear stability analysis of the steady simple shear flow solution is also carried out showing that there are regions of the parameter space where the steady solution becomes linearly unstable.
{"title":"Non-Newtonian rheology in inertial suspensions of inelastic rough hard spheres under simple shear flow","authors":"Rubén Gómez González, V. Garz'o","doi":"10.1063/5.0015241","DOIUrl":"https://doi.org/10.1063/5.0015241","url":null,"abstract":"Non-Newtonian transport properties of an inertial suspension of inelastic rough hard spheres under simple shear flow are determined from the Boltzmann kinetic equation. The influence of the interstitial gas on rough hard spheres is modeled via a Fokker-Planck generalized equation for rotating spheres accounting for the coupling of both the translational and rotational degrees of freedom of grains with the background viscous gas. The generalized Fokker-Planck term is the sum of two ordinary Fokker-Planck differential operators in linear $mathbf{v}$ and angular $boldsymbol{omega}$ velocity space. As usual, each Fokker-Planck operator is constituted by a drag force term (proportional to $mathbf{v}$ and/or $boldsymbol{omega}$) plus a stochastic Langevin term defined in terms of the background temperature $T_text{ex}$. The Boltzmann equation is solved by two different but complementary approaches: (i) by means of Grad's moment method, and (ii) by using a Bhatnagar-Gross-Krook (BGK)-type kinetic model adapted to inelastic rough hard spheres. As occurs in the case of emph{smooth} inelastic hard spheres, our results show that both the temperature and the non-Newtonian viscosity increase drastically with increasing the shear rate (discontinuous shear thickening effect) while the fourth-degree velocity moments also exhibit an $S$-shape. In particular, while high levels of roughness may slightly attenuate the jump of the viscosity in comparison to the smooth case, the opposite happens for the rotational temperature. As an application of these results, a linear stability analysis of the steady simple shear flow solution is also carried out showing that there are regions of the parameter space where the steady solution becomes linearly unstable.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83890619","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 : 2020-05-24DOI: 10.21468/SCIPOSTPHYS.9.4.050
Nina Javerzat, S. Grijalva, A. Rosso, R. Santachiara
We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites is usually denoted as the excursion set. The connected components of this set, the level clusters, define a one-parameter ($H$) family of percolation models with long-range correlation in the site occupation. The level clusters percolate at a finite value $h=h_c$ and for $Hleq-frac{3}{4}$ the phase transition is expected to remain in the same universality class of the pure (i.e. uncorrelated) percolation. For $-frac{3}{4}
{"title":"Topological effects and conformal invariance in long-range correlated random surfaces","authors":"Nina Javerzat, S. Grijalva, A. Rosso, R. Santachiara","doi":"10.21468/SCIPOSTPHYS.9.4.050","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYS.9.4.050","url":null,"abstract":"We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites is usually denoted as the excursion set. The connected components of this set, the level clusters, define a one-parameter ($H$) family of percolation models with long-range correlation in the site occupation. The level clusters percolate at a finite value $h=h_c$ and for $Hleq-frac{3}{4}$ the phase transition is expected to remain in the same universality class of the pure (i.e. uncorrelated) percolation. For $-frac{3}{4}<H< 0$ instead, there is a line of critical points with continously varying exponents. The universality class of these points, in particular concerning the conformal invariance of the level clusters, is poorly understood. By combining the Conformal Field Theory and the numerical approach, we provide new insights on these phases. We focus on the connectivity function, defined as the probability that two sites belong to the same level cluster. In our simulations, the surfaces are defined on a lattice torus of size $Mtimes N$. We show that the topological effects on the connectivity function make manifest the conformal invariance for all the critical line $H<0$. In particular, exploiting the anisotropy of the rectangular torus ($Mneq N$), we directly test the presence of the two components of the traceless stress-energy tensor. Moreover, we probe the spectrum and the structure constants of the underlying Conformal Field Theory. Finally, we observed that the corrections to the scaling clearly point out a breaking of integrability moving from the pure percolation point to the long-range correlated one.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87212701","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 : 2020-05-22DOI: 10.1103/PhysRevResearch.2.023216
Lennart Dabelow, P. Reimann
We consider quantum many-body systems evolving under a time-independent Hamiltonian $H$ from a nonequilibrium initial state at time $t=0$ towards a close-to-equilibrium state at time $t=tau$. Subsequently, this state is slightly perturbed and finally propagated for another time period $tau$ under the inverted Hamiltonian $-H$. The entire procedure may also be viewed as an imperfect time inversion or "echo dynamics". We unravel a remarkable persistence of such dynamics with respect to the observable deviations of the time-dependent expectation values from the equilibrium expectation value: For most perturbations, the deviations in the final state are essentially independent of the inversion time point $tau$. Our quantitative analytical predictions compare very well with exact numerical results.
{"title":"Persistent many-body quantum echoes","authors":"Lennart Dabelow, P. Reimann","doi":"10.1103/PhysRevResearch.2.023216","DOIUrl":"https://doi.org/10.1103/PhysRevResearch.2.023216","url":null,"abstract":"We consider quantum many-body systems evolving under a time-independent Hamiltonian $H$ from a nonequilibrium initial state at time $t=0$ towards a close-to-equilibrium state at time $t=tau$. Subsequently, this state is slightly perturbed and finally propagated for another time period $tau$ under the inverted Hamiltonian $-H$. The entire procedure may also be viewed as an imperfect time inversion or \"echo dynamics\". We unravel a remarkable persistence of such dynamics with respect to the observable deviations of the time-dependent expectation values from the equilibrium expectation value: For most perturbations, the deviations in the final state are essentially independent of the inversion time point $tau$. Our quantitative analytical predictions compare very well with exact numerical results.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74940929","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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