4.6 Article

On conservation laws, relaxation and pre-relaxation after a quantum quench

Publisher

IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2014/03/P03016

Keywords

symmetries of integrable models; stationary states; quantum quenches; thermalization

Funding

  1. EPSRC [EP/I032487/1, EP/J014885/1]
  2. EPSRC [EP/I032487/1, EP/J014885/1] Funding Source: UKRI
  3. Engineering and Physical Sciences Research Council [EP/I032487/1, EP/J014885/1] Funding Source: researchfish

Ask authors/readers for more resources

We consider the time evolution following a quantum quench in spin-1/2 chains. It is well known that local conservation laws constrain the dynamics and. eventually, the stationary behavior of local observables. We show that some widely studied models, such as the quantum XY model, possess extra families of local conservation laws in addition to the translation in ones. As a consequence, the additional charges must be included in the generalized Gibbs ensemble that, describes the stationary properties. The effects go well beyond a simple redefinition of the stationary state. The time evolution of a non-translation-invariant state under a (translation-invariant) Hamiltonian with a perturbation that weakly breaks the hidden symmetries underlying the extra conservation laws exhibits pre-relaxation. In addition, in the limit of small perturbation, the tune evolution following pre-relaxation can be described by means of a time-dependent generalized Gibbs ensemble.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.6
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

Article Physics, Multidisciplinary

Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents

Maurizio Fagotti

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2017)

Article Physics, Multidisciplinary

Prethermalization at Low Temperature: The Scent of Long-Range Order

Vincenzo Alba, Maurizio Fagotti

PHYSICAL REVIEW LETTERS (2017)

Article Physics, Multidisciplinary

Entanglement evolution and generalised hydrodynamics: noninteracting systems

Bruno Bertini, Maurizio Fagotti, Lorenzo Piroli, Pasquale Calabrese

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2018)

Article Mechanics

Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects

Vincenzo Alba, Bruno Bertini, Maurizio Fagotti, Lorenzo Piroli, Paola Ruggiero

Summary: This paper provides a pedagogical introduction to the generalized hydrodynamic approach in inhomogeneous quenches in integrable many-body quantum systems, focusing on applications to bipartitioning protocols and trap quenches. Exact results for time-dependent correlation functions and entanglement evolution are discussed, as well as the theory's range of applicability, open questions, and future directions.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2021)

Article Physics, Multidisciplinary

Global Quenches after Localized Perturbations

Maurizio Fagotti

Summary: We investigate the effect of a single spin flip preceding a global quench between translationally invariant local Hamiltonians in spin-1/2 chains. The effect of the localized perturbation does not fade away however large the distance from the perturbation is. In particular, translational invariance is not restored and the infinite-time limit depends on whether the spin was flipped or not. We argue that this phenomenon is more general than the particular example considered and we conjecture that it is triggered by topological properties, specifically, the existence of semilocal charges.

PHYSICAL REVIEW LETTERS (2022)

Article Physics, Multidisciplinary

Macroscopic Effects of Localized Measurements in Jammed States of Quantum Spin Chains

Kemal Bidzhiev, Maurizio Fagotti, Lenart Zadnik

Summary: This paper investigates the properties of quantum jammed state and its time evolution. By performing localized measurement in a jammed state, it is found that jamming is locally restored, but local observables exhibit nontrivial time evolution on macroscopic scales, without returning to their initial values.

PHYSICAL REVIEW LETTERS (2022)

Article Physics, Multidisciplinary

Measurement catastrophe and ballistic spread of charge density with vanishing current

L. Zadnik, S. Bocini, K. Bidzhiev, M. Fagotti

Summary: This study investigates the stationary states of many-body quantum systems with Hilbert-space fragmentation, revealing that these states have long-lasting macroscopic effects when measured. The research provides a clear example of the expectation value of charge density becoming a nontrivial function of the ratio between distance and time at late times, despite the corresponding current approaching zero.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2022)

Article Physics, Multidisciplinary

The folded spin-1/2 XXZ model: II. Thermodynamics and hydrodynamics with a minimal set of charges

Lenart Zadnik, Kemal Bidzhiev, Maurizio Fagotti

Summary: The study focuses on the dual folded spin-1/2 XXZ model in the thermodynamic limit, particularly on a class of local macrostates including Gibbs ensembles. A thermodynamic Bethe Ansatz description is developed, and generalized hydrodynamics is worked out at the leading order. Interestingly, in the ballistic scaling limit, the junction of two local macrostates results in a discontinuity in the profile of essentially any local observable.

SCIPOST PHYSICS (2021)

Article Physics, Multidisciplinary

The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties

Lenart Zadnik, Maurizio Fagotti

Summary: The study focuses on an effective Hamiltonian that describes the time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. The model, to leading order, is integrable with local interactions. Using a coordinate Bethe Ansatz, the authors solve the model completely, demonstrating the existence of exponentially many jammed states and estimating their stability under the leading correction to the effective Hamiltonian. Ground state properties of the model are also discussed.

SCIPOST PHYSICS CORE (2021)

Article Physics, Multidisciplinary

Locally quasi-stationary states in noninteracting spin chains

Maurizio Fagotti

SCIPOST PHYSICS (2020)

Article Physics, Multidisciplinary

Entanglement evolution and generalised hydrodynamics: interacting integrable systems

Vincenzo Alba, Bruno Bertini, Maurizio Fagotti

SCIPOST PHYSICS (2019)

Article Physics, Multidisciplinary

On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system

Maurizio Fagotti

SCIPOST PHYSICS (2019)

Article Materials Science, Multidisciplinary

Higher-order generalized hydrodynamics in one dimension: The noninteracting test

Maurizio Fagotti

PHYSICAL REVIEW B (2017)

Article Materials Science, Multidisciplinary

Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions

Lorenzo Piroli, Jacopo De Nardis, Mario Collura, Bruno Bertini, Maurizio Fagotti

PHYSICAL REVIEW B (2017)

Article Optics

Entanglement growth and correlation spreading with variable-range interactions in spin and fermionic tunneling models

Anton S. Buyskikh, Maurizio Fagotti, Johannes Schachenmayer, Fabian Essler, Andrew J. Daley

PHYSICAL REVIEW A (2016)

No Data Available