Dynamical phase transitions in the two-dimensional transverse-field Ising model

Hashizume, Tomohiro; McCulloch, Ian P.; Halimeh, Jad C.

doi:10.1103/physrevresearch.4.013250

Cited by 40 publications

(26 citation statements)

References 68 publications

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“…In general, DPTs-II have a completely different origin than DPTs-I. Connections between both kinds of DPTs seem to exist in several systems of different nature [32,33,[35][36][37][38][39][40], e.g. the non-analytical points of DPTs-II have been linked with zeros of the order parameters of DPTs-I.…”

Section: Dpt-ii: Return Probabilitymentioning

confidence: 99%

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Dynamical and excited-state quantum phase transitions in collective systems

Corps,

Relaño

2022

Preprint

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We study dynamical phase transitions (DPTs) in quantum many-body systems with infinite-range interaction, and present a theory connecting the two kinds of known DPTs (sometimes referred to as DPTs-I and DPTs-II) with the concept of excited-state quantum phase transition (ESQPT), traditionally found in collective models. We show that DPTs-I appear as a manifestation of symmetry restoration after a quench from the broken-symmetry phase, the limits between these two phases being demarcated precisely by an ESQPT. We describe the order parameters of DPTs-I with a generalization of the standard microcanonical ensemble incorporating the information of an additional conserved charge identifying the corresponding phase. We also show that DPTs-I are linked to a mechanism of information erasure brought about by the ESQPT, and quantify this information loss with the statistical ensemble that we propose. Finally, we show analytically that DPTs-II are forbidden in these systems for quenches leading a broken-symmetry initial state to the same broken-symmetry phase, on one side of the ESQPT, and we provide a formulation of DPTs-II depending on the side of the ESQPT where the quench ends. We analyze the connections between various indicators of DPTs-II. Our results are numerically illustrated in the infinite-range transverse-field Ising model and are applicable to a large class of collective quantum systems satisfying a set of conditions.

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Section: Dpt-ii: Return Probabilitymentioning

confidence: 99%

“…Indeed, it is known that both DPTs-I and DPTs-II can take place in the same models, like the fully connected transverse-field Ising model [32,33], or the Rabi model [34]. Connections between both kinds of DPTs have been proposed [32,33,[35][36][37][38][39][40]; nevertheless, a common triggering mechanism has not been found.…”

Section: Introductionmentioning

confidence: 99%

Dynamical and excited-state quantum phase transitions in collective systems

Corps,

Relaño

2022

Preprint

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“…The growth of entanglement becomes even more severe in spatial dimensions larger than one. Despite recent advances involving MPS-based or tensor-network algorithms [48][49][50][51][52][53], as well as the advent of innovative machine-learning approaches [54][55][56], the time scales numerically attainable for two-dimensional quantum many-body systems are still comparatively short. While the dynamics of such two-dimensional systems can nowadays be accessed in experiments with quantum simulators [57][58][59], the development of efficient numerical techniques is paramount.…”

Section: Conclusion 13mentioning

confidence: 99%

“…On the other hand, for a two-dimensional square lattice, H is nonintegrable [24,25,61], and the quantum phase transition between an ordered phase and an unordered phase occurs at the larger transverse field g = g c ≈ 3.044 [62]. For intermediate cases, such as "semi-infinite" multi-leg ladders on a cylinder geometry, the exact value of g c can vary due to finite-size corrections [50].…”

Section: Models Observables and Quench Protocolsmentioning

confidence: 99%

“…We now come to the last part of this paper, i.e., the quantum quench dynamics in the two-dimensional transverse-field Ising model. Note that dynamical properties of this model [50,52,56,58,98,99], as well as the emergence of thermalization [24,25,61], have been studied before by a variety of approaches. By comparing our results to existing data from the literature, let us demonstrate in this section that numerical linked cluster expansions based on rectangular clusters only, combined with an efficient forward propagation of pure states, provide a competitive alternative to other state-of-the-art numerical approaches.…”

Section: Two-dimensional Square Latticementioning

confidence: 99%

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Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters

Richter,

Heitmann,

Steinigeweg

2020

Preprint

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We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two-and three-leg ladders, and twodimensional square lattices. Starting from fully polarized initial states, we consider the dynamics of the transverse and the longitudinal magnetization for quenches to weak, strong, and critical values of the transverse field. To this end, we rely on an efficient combination of numerical linked cluster expansions (NLCEs) and a forward propagation of pure states in real time. As a main result, we demonstrate that NLCEs comprising solely rectangular clusters provide a promising approach to study the real-time dynamics of two-dimensional quantum many-body systems directly in the thermodynamic limit. By comparing to existing data from the literature, we unveil that NLCEs yield converged results on time scales which are competitive to other state-of-the-art numerical methods.

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A lattice model for condensation in Levin-Wen systems

Christian,

Green,

Huston

et al. 2023

J. High Energ. Phys.

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Levin-Wen string-net models provide a construction of (2+1)D topologically ordered phases of matter with anyonic localized excitations described by the Drinfeld center of a unitary fusion category. Anyon condensation is a mechanism for phase transitions between (2+1)D topologically ordered phases. We construct an extension of Levin-Wen models in which tuning a parameter implements anyon condensation. We also describe the classification of anyons in Levin-Wen models via representation theory of the tube algebra, and use a variant of the tube algebra to classify low-energy localized excitations in the condensed phase.

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Dynamical phase transitions in the two-dimensional transverse-field Ising model

Cited by 40 publications

References 68 publications

Dynamical and excited-state quantum phase transitions in collective systems

Dynamical and excited-state quantum phase transitions in collective systems

Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters

A lattice model for condensation in Levin-Wen systems

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