Quantum quenches in the thermodynamic limit. II. Initial ground states

Rigol, Marcos

doi:10.1103/physreve.90.031301

Cited by 23 publications

(36 citation statements)

References 59 publications

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“…The question of thermalization can then reduce to the question of how narrow in energy the overlap distribution is. Recent work (such as the "quench action" approach [82][83][84][85][86][87][88] and an approach based on linked-cluster expansions [89,90]) has formulated calculations of long-time expectation values directly in the thermodynamic limit, thus avoiding the explicit calculation of overlaps in finite-size systems.…”

Section: O(t) = ψ(T)|o|ψ(t) = ψmentioning

confidence: 99%

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

et al. 2016

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The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e., by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

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Section: O(t) = ψ(T)|o|ψ(t) = ψmentioning

confidence: 99%

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

et al. 2016

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“…NLCEs can be used to study dynamics of pure and mixed (thermal equilibrium) states in arbitrary dimensions. They have been shown to be a powerful tool to study quantum systems in thermal equilibrium [29], entanglement entropy [30][31][32], diagonal ensemble predictions after quantum quenches from initial thermal [33] and pure [34][35][36] states, and for obtaining steady-state results in driven dissipative systems [37].…”

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confidence: 99%

Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit

Mallayya

Rigol

2018

Phys. Rev. Lett.

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We implement numerical linked cluster expansions (NLCEs) to study dynamics of lattice systems following quantum quenches, and focus on a hard-core boson model in one-dimensional lattices. We find that, in the nonintegrable regime and within the accessible times, local observables exhibit exponential relaxation. We determine the relaxation rate as one departs from the integrable point and show that it scales quadratically with the strength of the integrability breaking perturbation. We compare the NLCE results with those from exact diagonalization calculations on finite chains with periodic boundary conditions, and show that NLCEs are far more accurate.

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“…The order of the "maximally connected" NLCE is set by the number of sites of the largest cluster (note that there is only one cluster for each given number of sites) [45,47]. When only nearest neighbor interactions are present, this is the only NLCE possible for a 1D lattice [46,48,49]. Hence, this NLCE is expected to be best suited for weak next-nearest neighbor couplings.…”

Section: Numerical Linked Cluster Expansionsmentioning

confidence: 99%

“…Recently, a numerical linked cluster expansion (NLCE) approach was introduced that, when converged, allows one to calculate infinite-time averages of observables in the thermodynamic limit after quenches from initial thermal equilibrium [45] and pure [46] states. This approach was used to probe fundamental differences in quenches to and away from integrability starting from thermal states [47], and to study quantum quenches from Néel and tilted ferromagnetic states in the spin-1/2 XXZ chain [48,49].…”

Section: Introductionmentioning

confidence: 99%

“…This approach was used to probe fundamental differences in quenches to and away from integrability starting from thermal states [47], and to study quantum quenches from Néel and tilted ferromagnetic states in the spin-1/2 XXZ chain [48,49]. Its main limitation is that the expansion may fail to converge when the temperature of the initial state is low [45], as well as for Hamiltonian parameters of interest in quenches from pure states [46,48,49]. For systems in thermal equilibrium, it has been shown that NLCEs converge to lower temperatures than traditional high-temperature expansions [50], and exponentially faster than exact diagonalization calculations [51].…”

Section: Introductionmentioning

confidence: 99%

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Numerical linked cluster expansions for quantum quenches in one-dimensional lattices

Mallayya

Rigol

2017

Phys. Rev. E

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We discuss the application of numerical linked cluster expansions (NLCEs) to study one dimensional lattice systems in thermal equilibrium and after quantum quenches from thermal equilibrium states. For the former, we calculate observables in the grand canonical ensemble, while for the latter we calculate observables in the diagonal ensemble. When converged, NLCEs provide results in the thermodynamic limit. We use two different NLCEs -a maximally connected expansion introduced in previous works and a site-based expansion. We compare the effectiveness of both NLCEs. The site-based NLCE is found to work best for systems in thermal equilibrium. However, in thermal equilibrium and after quantum quenches, the site-based NLCE can diverge when the maximally connected one converges. We relate this divergence to the exponentially large number of graphs in the site-based NLCE and the behavior of the weights of observables in those graphs. We discuss the effectiveness of resummations to cure the divergence. Our NLCE calculations are compared to exact diagonalization ones in lattices with periodic boundary conditions. NLCEs are found to outperform exact diagonalization in periodic systems for all quantities studied.

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Quantum quenches in the thermodynamic limit. II. Initial ground states

Cited by 23 publications

References 59 publications

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit

Numerical linked cluster expansions for quantum quenches in one-dimensional lattices

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