Dynamics and transport at the threshold of many-body localization

Gopalakrishnan, Sarang; Parameswaran, S. A.

doi:10.1016/j.physrep.2020.03.003

Cited by 95 publications

(79 citation statements)

References 362 publications

(573 reference statements)

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“…Considering lower symmetry systems may, however, not only bring about complications but also allow for qualitatively new kinds of behavior. For instance, the study of systems with broken translation symmetry has brought to light the phenomena of Anderson and manybody localization, ultimately shaking up certain foundational beliefs of quantum statistical mechanics [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Fine structure of heating in a quasiperiodically driven critical quantum system

Lapierre

Choo

Tiwari

et al. 2020

Phys. Rev. Research

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We study the heating dynamics of a generic one-dimensional critical system when driven quasiperiodically. Specifically, we consider a Fibonacci drive sequence comprising the Hamiltonian of uniform conformal field theory (CFT) describing such critical systems and its sine-square deformed counterpart. The asymptotic dynamics is dictated by the Lyapunov exponent which has a fractal structure embedding Cantor lines where the exponent is exactly zero. Away from these Cantor lines, the system typically heats up fast to infinite energy in a nonergodic manner where the quasiparticle excitations congregate at a small number of select spatial locations resulting in a buildup of energy at these points. Periodic dynamics with no heating for physically relevant timescales is seen in the high-frequency regime. As we traverse the fractal region and approach the Cantor lines, the heating slows enormously and the quasiparticles completely delocalize at stroboscopic times. Our setup allows us to tune between fast and ultraslow heating regimes in integrable systems.

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Section: Introductionmentioning

confidence: 99%

Fine structure of heating in a quasiperiodically driven critical quantum system

Lapierre

Choo

Tiwari

et al. 2020

Phys. Rev. Research

View full text Add to dashboard Cite

show abstract

“…Note that the Gaussians (dashed lines) are no fit but are calculated from Eqs. (17) and (18). In the case with η = 0, an overall triangular shape survives even for long times, with some local fluctuations.…”

Section: A Limiting Casesmentioning

confidence: 93%

“…3(a) are no fit since the width (t ) has been calculated exactly according to Eq. (18); that is, there is no free parameter involved. In contrast, the profiles for η = 0 in Fig.…”

Section: A Limiting Casesmentioning

confidence: 99%

“…The dashed lines are Gaussian functions calculated from Eqs. (17) and (18). (a) At moderate imbalance η = 0.8, the profiles can be very well described by Gaussians.…”

Section: Spatial Widthmentioning

confidence: 99%

“…While the majority of studies on many-body localization (MBL) typically focus on one-dimensional and short-range models composed of, e.g., spin-1/2 degrees of freedom, there has been much effort recently to generalize the notion of MBL to a wider class of models [18]. This includes, e.g., systems which are weakly coupled to a thermal bath [19], models with long-range interactions [20] or degrees of freedom with higher spin S > 1/2 [21,22], and Hubbard models where the disorder couples only to either the charge or spin degree of freedom [23,24].…”

Section: Introductionmentioning

confidence: 99%

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Density dynamics in the mass-imbalanced Hubbard chain

et al. 2020

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We consider two mutually interacting fermionic particle species on a one-dimensional lattice and study how the mass ratio η between the two species affects the (equilibration) dynamics of the particles. Focusing on the regime of strong interactions and high temperatures, two well-studied points of reference are given by (i) the case of equal masses η = 1, i.e., the standard Fermi-Hubbard chain, where initial nonequilibrium density distributions are known to decay, and (ii) the case of one particle species being infinitely heavy, η = 0, leading to a localization of the lighter particles in an effective disorder potential. Given these two opposing cases, the dynamics in the case of intermediate mass ratios 0 < η < 1 is of particular interest. To this end, we study the real-time dynamics of pure states featuring a sharp initial nonequilibrium density profile. Relying on the concept of dynamical quantum typicality, the resulting nonequilibrium dynamics can be related to equilibrium correlation functions. Summarizing our main results, we observe that diffusive transport occurs for moderate values of the mass imbalance and manifests itself in a Gaussian spreading of real-space density profiles and an exponential decay of density modes in momentum space. For stronger imbalances, we provide evidence that transport becomes anomalous on intermediate timescales, and in particular, our results are consistent with the absence of strict localization in the long-time limit for any η > 0. Based on our numerical analysis, we provide an estimate for the "lifetime" of the effective localization as a function of η.

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Anomalies of average symmetries: entanglement and open quantum systems

Hsin,

Luo,

Sun

2024

J. High Energ. Phys.

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Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on average. This work investigates the constraints on mixed states resulting from non-commuting average symmetries. We will focus on the cases where the commutation relations of the average symmetry generators are violated by nontrivial phases, and call such average symmetry anomalous. We show that anomalous average symmetry implies degeneracy in the density matrix eigenvalues, and present several lattice examples with average symmetries, including XY chain, Heisenberg chain, and deformed toric code models. In certain cases, the results can be further extended to reduced density matrices, leading to a new lower bound on the entanglement entropy. We discuss several applications in the contexts of many body localization, quantum channels, entanglement phase transitions and also derive new constraints on the Lindbladian evolution of open quantum systems.

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Dynamics and transport at the threshold of many-body localization

Cited by 95 publications

References 362 publications

Fine structure of heating in a quasiperiodically driven critical quantum system

Fine structure of heating in a quasiperiodically driven critical quantum system

Density dynamics in the mass-imbalanced Hubbard chain

Anomalies of average symmetries: entanglement and open quantum systems

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