We present a numerical model that simulates the current-voltage (I-V) characteristics of materials that exhibit percolation conduction. The model consists of a two dimensional grid of exponentially different resistors in the presence of an external electric field. We obtained exponentially non-ohmic I-V characteristics validating earlier analytical predictions and consistent with multiple experimental observations of the Poole-Frenkel laws in non-crystalline materials. The exponents are linear in voltage for samples smaller than the correlation length of percolation cluster L, and square root in voltage for samples larger than L.
{"title":"Numerical modeling of nonohmic percolation conduction and Poole–Frenkel laws","authors":"Maria Patmiou, V. G. Karpov, G. Serpen, B. Weborg","doi":"10.1063/5.0019844","DOIUrl":"https://doi.org/10.1063/5.0019844","url":null,"abstract":"We present a numerical model that simulates the current-voltage (I-V) characteristics of materials that exhibit percolation conduction. The model consists of a two dimensional grid of exponentially different resistors in the presence of an external electric field. We obtained exponentially non-ohmic I-V characteristics validating earlier analytical predictions and consistent with multiple experimental observations of the Poole-Frenkel laws in non-crystalline materials. The exponents are linear in voltage for samples smaller than the correlation length of percolation cluster L, and square root in voltage for samples larger than L.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"206 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74132627","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 : 2020-06-08DOI: 10.1103/physrevresearch.2.043346
Ivan M Khaymovich, V. Kravtsov, B. Altshuler, L. Ioffe
In this paper we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We argue that this model is more suitable to describe a generic many body localization problem. In contrast to RP model, in LN-RP model a new, weakly ergodic phase appears that is characterized by the broken basis-rotation symmetry which the fully-ergodic phase respects. Therefore, in addition to the localization and ergodic transitions in LN-RP model there exists also the transition between the two ergodic phases (FWE transition). We suggest new criteria of stability of the non-ergodic phases which give the points of localization and ergodic transitions and prove that the Anderson localization transition in LN-RP model is discontinuous, in contrast to that in a conventional RP model. We also formulate the criterion of FWE transition and obtain the full phase diagram of the model. We show that truncation of the log-normal tail shrinks the region of weakly-ergodic phase and restores the multifractal and the fully-ergodic phases.
{"title":"Fragile extended phases in the log-normal Rosenzweig-Porter model","authors":"Ivan M Khaymovich, V. Kravtsov, B. Altshuler, L. Ioffe","doi":"10.1103/physrevresearch.2.043346","DOIUrl":"https://doi.org/10.1103/physrevresearch.2.043346","url":null,"abstract":"In this paper we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We argue that this model is more suitable to describe a generic many body localization problem. In contrast to RP model, in LN-RP model a new, weakly ergodic phase appears that is characterized by the broken basis-rotation symmetry which the fully-ergodic phase respects. Therefore, in addition to the localization and ergodic transitions in LN-RP model there exists also the transition between the two ergodic phases (FWE transition). We suggest new criteria of stability of the non-ergodic phases which give the points of localization and ergodic transitions and prove that the Anderson localization transition in LN-RP model is discontinuous, in contrast to that in a conventional RP model. We also formulate the criterion of FWE transition and obtain the full phase diagram of the model. We show that truncation of the log-normal tail shrinks the region of weakly-ergodic phase and restores the multifractal and the fully-ergodic phases.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"132 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79656524","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 : 2020-05-23DOI: 10.1103/PHYSREVRESEARCH.2.043108
S. Sinha, Subhadeep Roy, A. Hansen
We study the effect of the competition between disorder and stress enhancement in fracture processes using the local load sharing fiber bundle model, a model that hovers on the border between analytical tractability and numerical accessibility. We implement a disorder distribution with one adjustable parameter. The model undergoes a localization transition as a function of this parameter. We identify an order parameter for this transition and find that the system is in the localized phase over a finite range of values of the parameter bounded by a transition to the non-localized phase on both sides. The transition is first order at the lower transition and second order at the upper transition. The critical exponents characterizing the second order transition are close to those characterizing the percolation transition. We determine the spatiotemporal correlation function in the localized phase. It is characterized by two power laws as in invasion percolation. We find exponents that are consistent with the values found in that problem.
{"title":"Phase transitions and correlations in fracture processes where disorder and stress compete","authors":"S. Sinha, Subhadeep Roy, A. Hansen","doi":"10.1103/PHYSREVRESEARCH.2.043108","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.2.043108","url":null,"abstract":"We study the effect of the competition between disorder and stress enhancement in fracture processes using the local load sharing fiber bundle model, a model that hovers on the border between analytical tractability and numerical accessibility. We implement a disorder distribution with one adjustable parameter. The model undergoes a localization transition as a function of this parameter. We identify an order parameter for this transition and find that the system is in the localized phase over a finite range of values of the parameter bounded by a transition to the non-localized phase on both sides. The transition is first order at the lower transition and second order at the upper transition. The critical exponents characterizing the second order transition are close to those characterizing the percolation transition. We determine the spatiotemporal correlation function in the localized phase. It is characterized by two power laws as in invasion percolation. We find exponents that are consistent with the values found in that problem.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81726781","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 : 2020-05-20DOI: 10.21468/SCIPOSTPHYS.10.2.044
F. Pietracaprina, F. Alet
We numerically study the possibility of many-body localization transition in a disordered quantum dimer model on the honeycomb lattice. By using the peculiar constraints of this model and state-of-the-art exact diagonalization and time evolution methods, we probe both eigenstates and dynamical properties and conclude on the existence of a localization transition, on the available time and length scales (system sizes of up to N=108 sites). We critically discuss these results and their implications.
{"title":"Probing many-body localization in a disordered quantum dimer model on the honeycomb lattice","authors":"F. Pietracaprina, F. Alet","doi":"10.21468/SCIPOSTPHYS.10.2.044","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYS.10.2.044","url":null,"abstract":"We numerically study the possibility of many-body localization transition in a disordered quantum dimer model on the honeycomb lattice. By using the peculiar constraints of this model and state-of-the-art exact diagonalization and time evolution methods, we probe both eigenstates and dynamical properties and conclude on the existence of a localization transition, on the available time and length scales (system sizes of up to N=108 sites). We critically discuss these results and their implications.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"110 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76302732","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 study the site-diluted double exchange (DE) model and its effective Ruderman-Kittel-Kasuya-Yosida-like interactions, where localized spins are randomly distributed, with the use of the Self-learning Monte Carlo (SLMC) method. The SLMC method is an accelerating technique for Markov chain Monte Carlo simulation using trainable effective models. We apply the SLMC method to the site-diluted DE model to explore the utility of the SLMC method for random systems. We check the acceptance ratios and investigate the properties of the effective models in the strong coupling regime. The effective two-body spin-spin interaction in the site-diluted DE model can describe the original DE model with a high acceptance ratio, which depends on temperatures and spin concentration. These results support a possibility that the SLMC method could obtain independent configurations in systems with a critical slowing down near a critical temperature or in random systems where a freezing problem occurs in lower temperatures.
{"title":"Effective Ruderman–Kittel–Kasuya–Yosida-like Interaction in Diluted Double-exchange Model: Self-learning Monte Carlo Approach","authors":"Hidehiko Kohshiro, Y. Nagai","doi":"10.7566/JPSJ.90.034711","DOIUrl":"https://doi.org/10.7566/JPSJ.90.034711","url":null,"abstract":"We study the site-diluted double exchange (DE) model and its effective Ruderman-Kittel-Kasuya-Yosida-like interactions, where localized spins are randomly distributed, with the use of the Self-learning Monte Carlo (SLMC) method. The SLMC method is an accelerating technique for Markov chain Monte Carlo simulation using trainable effective models. We apply the SLMC method to the site-diluted DE model to explore the utility of the SLMC method for random systems. We check the acceptance ratios and investigate the properties of the effective models in the strong coupling regime. The effective two-body spin-spin interaction in the site-diluted DE model can describe the original DE model with a high acceptance ratio, which depends on temperatures and spin concentration. These results support a possibility that the SLMC method could obtain independent configurations in systems with a critical slowing down near a critical temperature or in random systems where a freezing problem occurs in lower temperatures.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85505585","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 : 2020-05-12DOI: 10.1103/PHYSREVRESEARCH.2.043241
Wenlong Wang, M. Wallin, J. Lidmar
We present a large-scale simulation of the three-dimensional Ising spin glass with Gaussian disorder to low temperatures and large sizes using optimized population annealing Monte Carlo. Our primary focus is investigating the number of pure states regarding a controversial statistic, characterizing the fraction of centrally peaked disorder instances, of the overlap function order parameter. We observe that this statistic is subtly and sensitively influenced by the slight fluctuations of the integrated central weight of the disorder-averaged overlap function, making the asymptotic growth behaviour very difficult to identify. Modified statistics effectively reducing this correlation are studied and essentially monotonic growth trends are obtained. The effect of temperature is also studied, finding a larger growth rate at a higher temperature. Our detailed examination and state-of-the-art simulation provide a coherent picture of many pure states, explain the previous findings, and the controversy is solved. The pertinent status of the number of pure states beyond this statistic is also discussed, and we find the spin glass balance is overall tilting towards many pure states studied by simulations.
{"title":"Evidence of many thermodynamic states of the three-dimensional Ising spin glass","authors":"Wenlong Wang, M. Wallin, J. Lidmar","doi":"10.1103/PHYSREVRESEARCH.2.043241","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.2.043241","url":null,"abstract":"We present a large-scale simulation of the three-dimensional Ising spin glass with Gaussian disorder to low temperatures and large sizes using optimized population annealing Monte Carlo. Our primary focus is investigating the number of pure states regarding a controversial statistic, characterizing the fraction of centrally peaked disorder instances, of the overlap function order parameter. We observe that this statistic is subtly and sensitively influenced by the slight fluctuations of the integrated central weight of the disorder-averaged overlap function, making the asymptotic growth behaviour very difficult to identify. Modified statistics effectively reducing this correlation are studied and essentially monotonic growth trends are obtained. The effect of temperature is also studied, finding a larger growth rate at a higher temperature. Our detailed examination and state-of-the-art simulation provide a coherent picture of many pure states, explain the previous findings, and the controversy is solved. The pertinent status of the number of pure states beyond this statistic is also discussed, and we find the spin glass balance is overall tilting towards many pure states studied by simulations.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89312995","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 : 2020-05-05DOI: 10.1103/PHYSREVRESEARCH.2.042025
Vishnu V. Krishnan, S. Karmakar, K. Ramola
We show that the distribution of elements $H$ in the Hessian matrices associated with amorphous materials exhibit cusp singularities $P(H) sim {lvert H rvert}^{gamma}$ with an exponent $gamma < 0$, as $lvert H rvert to 0$. We exploit the rotational invariance of the underlying disorder in amorphous structures to derive these exponents exactly for systems interacting via radially symmetric potentials. We show that $gamma$ depends only on the degree of smoothness $n$ of the potential of interaction between the constituent particles at the cut-off distance, independent of the details of interaction in both two and three dimensions. We verify our predictions with numerical simulations of models of structural glass formers. Finally, we show that such cusp singularities affect the stability of amorphous solids, through the distributions of the minimum eigenvalue of the Hessian matrix.
我们表明，在与非晶材料相关的Hessian矩阵中，元素$H$的分布表现出顶点奇点$P(H) sim {lvert H rvert}^{gamma}$，其指数为$gamma < 0$，为$lvert H rvert to 0$。我们利用非晶结构中潜在无序的转动不变性，精确地推导出通过径向对称势相互作用的系统的这些指数。我们表明$gamma$仅取决于组成粒子之间在截止距离处的相互作用势的平滑程度$n$，而与二维和三维相互作用的细节无关。我们用结构玻璃成形器模型的数值模拟验证了我们的预测。最后，我们通过Hessian矩阵最小特征值的分布证明了这种尖点奇点影响非晶固体的稳定性。
{"title":"Singularities in Hessian element distributions of amorphous media","authors":"Vishnu V. Krishnan, S. Karmakar, K. Ramola","doi":"10.1103/PHYSREVRESEARCH.2.042025","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.2.042025","url":null,"abstract":"We show that the distribution of elements $H$ in the Hessian matrices associated with amorphous materials exhibit cusp singularities $P(H) sim {lvert H rvert}^{gamma}$ with an exponent $gamma < 0$, as $lvert H rvert to 0$. We exploit the rotational invariance of the underlying disorder in amorphous structures to derive these exponents exactly for systems interacting via radially symmetric potentials. We show that $gamma$ depends only on the degree of smoothness $n$ of the potential of interaction between the constituent particles at the cut-off distance, independent of the details of interaction in both two and three dimensions. We verify our predictions with numerical simulations of models of structural glass formers. Finally, we show that such cusp singularities affect the stability of amorphous solids, through the distributions of the minimum eigenvalue of the Hessian matrix.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"83 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83798171","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}
Vladimir Vargas-Calderón, H. Vinck-Posada, F. A. Gonz'alez
Recently, the use of neural quantum states for describing the ground state of many- and few-body problems has been gaining popularity because of their high expressivity and ability to handle intractably large Hilbert spaces. In particular, methods based on variational Monte Carlo have proven to be successful in describing the physics of bosonic systems such as the Bose-Hubbard model. However, this technique has not been systematically tested on the parameter space of the Bose-Hubbard model, particularly at the boundary between the Mott insulator and superfluid phases. In this work, we evaluate the capabilities of variational Monte Carlo with a trial wavefunction given by a Restricted Boltzmann Machine to reproduce the quantum ground state of the Bose-Hubbard model on several points of its parameter space. To benchmark the technique, we compare its results to the ground state found through exact diagonalization for small one-dimensional chains. In general, we find that the learned ground state correctly estimates many observables, reproducing to a high degree the phase diagram for the first Mott lobe and part of the second one. However, we find that the technique is challenged whenever the system transitions between excitation manifolds, as the ground state is not learned correctly at these boundaries. Nonetheless, we propose a method to discard noisy probabilities learned in the ground state, which improves the quality of the results produced by the method.
{"title":"Phase Diagram Reconstruction of the Bose–Hubbard Model with a Restricted Boltzmann Machine Wavefunction","authors":"Vladimir Vargas-Calderón, H. Vinck-Posada, F. A. Gonz'alez","doi":"10.7566/JPSJ.89.094002","DOIUrl":"https://doi.org/10.7566/JPSJ.89.094002","url":null,"abstract":"Recently, the use of neural quantum states for describing the ground state of many- and few-body problems has been gaining popularity because of their high expressivity and ability to handle intractably large Hilbert spaces. In particular, methods based on variational Monte Carlo have proven to be successful in describing the physics of bosonic systems such as the Bose-Hubbard model. However, this technique has not been systematically tested on the parameter space of the Bose-Hubbard model, particularly at the boundary between the Mott insulator and superfluid phases. In this work, we evaluate the capabilities of variational Monte Carlo with a trial wavefunction given by a Restricted Boltzmann Machine to reproduce the quantum ground state of the Bose-Hubbard model on several points of its parameter space. To benchmark the technique, we compare its results to the ground state found through exact diagonalization for small one-dimensional chains. In general, we find that the learned ground state correctly estimates many observables, reproducing to a high degree the phase diagram for the first Mott lobe and part of the second one. However, we find that the technique is challenged whenever the system transitions between excitation manifolds, as the ground state is not learned correctly at these boundaries. Nonetheless, we propose a method to discard noisy probabilities learned in the ground state, which improves the quality of the results produced by the method.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74552108","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}
Advances in predictive modeling across multiple disciplines have yielded generative models capable of high veracity in predicting macroscopic functional responses of materials. Correspondingly, of interest is the inverse problem of finding the model parameter that will yield desired macroscopic responses, such as stress-strain curves, ferroelectric hysteresis loops, etc. Here we suggest and implement a Gaussian Process based methods that allow to effectively sample the degenerate parameter space of a complex non-local model to output regions of parameter space which yield desired functionalities. We discuss the specific adaptation of the acquisition function and sampling function to make the process efficient and balance the efficient exploration of parameter space for multiple possible minima and exploitation to densely sample the regions of interest where target behaviors are optimized. This approach is illustrated via the hysteresis loop engineering in ferroelectric materials, but can be adapted to other functionalities and generative models. The code is open-sourced and available at [this http URL].
{"title":"Guided search for desired functional responses via Bayesian optimization of generative model: Hysteresis loop shape engineering in ferroelectrics","authors":"Sergei V. Kalinin, M. Ziatdinov, R. Vasudevan","doi":"10.1063/5.0011917","DOIUrl":"https://doi.org/10.1063/5.0011917","url":null,"abstract":"Advances in predictive modeling across multiple disciplines have yielded generative models capable of high veracity in predicting macroscopic functional responses of materials. Correspondingly, of interest is the inverse problem of finding the model parameter that will yield desired macroscopic responses, such as stress-strain curves, ferroelectric hysteresis loops, etc. Here we suggest and implement a Gaussian Process based methods that allow to effectively sample the degenerate parameter space of a complex non-local model to output regions of parameter space which yield desired functionalities. We discuss the specific adaptation of the acquisition function and sampling function to make the process efficient and balance the efficient exploration of parameter space for multiple possible minima and exploitation to densely sample the regions of interest where target behaviors are optimized. This approach is illustrated via the hysteresis loop engineering in ferroelectric materials, but can be adapted to other functionalities and generative models. The code is open-sourced and available at [this http URL].","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83707858","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 : 2020-04-24DOI: 10.1103/physrevresearch.2.043368
S. Thomson, M. Schirò
A number of experimental platforms for quantum simulations of disordered quantum matter, from dipolar systems to trapped ions, involve degrees of freedom which are coupled by power-law decaying hoppings or interactions, yet the interplay of disorder and interactions in these systems is far less understood than in their short-ranged counterpart. Here we consider a prototype model of interacting fermions with disordered long-ranged hoppings and interactions, and use the flow equation approach to map out its dynamical phase diagram as a function of hopping and interaction exponents. We demonstrate that the flow equation technique is ideally suited to problems involving long-range couplings due to its ability to accurately simulate very large system sizes. We show that, at large on-site disorder and for short-range interactions, a transition from a delocalized phase to a quasi many-body localized (MBL) phase exists as the hopping range is decreased. This quasi-MBL phase is characterized by intriguing properties such as a set of emergent conserved quantities which decay algebraically with distance. Surprisingly we find that a crossover between delocalized and quasi-MBL phases survives even in the presence of long-range interactions.
{"title":"Quasi-many-body localization of interacting fermions with long-range couplings","authors":"S. Thomson, M. Schirò","doi":"10.1103/physrevresearch.2.043368","DOIUrl":"https://doi.org/10.1103/physrevresearch.2.043368","url":null,"abstract":"A number of experimental platforms for quantum simulations of disordered quantum matter, from dipolar systems to trapped ions, involve degrees of freedom which are coupled by power-law decaying hoppings or interactions, yet the interplay of disorder and interactions in these systems is far less understood than in their short-ranged counterpart. Here we consider a prototype model of interacting fermions with disordered long-ranged hoppings and interactions, and use the flow equation approach to map out its dynamical phase diagram as a function of hopping and interaction exponents. We demonstrate that the flow equation technique is ideally suited to problems involving long-range couplings due to its ability to accurately simulate very large system sizes. We show that, at large on-site disorder and for short-range interactions, a transition from a delocalized phase to a quasi many-body localized (MBL) phase exists as the hopping range is decreased. This quasi-MBL phase is characterized by intriguing properties such as a set of emergent conserved quantities which decay algebraically with distance. Surprisingly we find that a crossover between delocalized and quasi-MBL phases survives even in the presence of long-range interactions.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81563672","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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