Stationary states in a free fermionic chain from the quench action method

Luca, Andrea De; Martelloni, Gianluca; Viti, Jacopo

doi:10.1103/physreva.91.021603

Cited by 65 publications

(70 citation statements)

References 53 publications

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“…The computations of [22,23] seem to indicate that in the presence of conserved charges the universality of (at least) the low pressure behavior of the steady state breaks down. Carrying out a holographic computation with conserved charges may shed light on the possible late time behavior of charged configurations.…”

Section: Discussionmentioning

confidence: 99%

Black brane steady states

Amado

Yarom

2015

J. High Energ. Phys.

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Section: Discussionmentioning

confidence: 99%

Black brane steady states

Amado

Yarom

2015

J. High Energ. Phys.

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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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“…In the semiclassical limit, the function h(x, t) is again a scaling function h(x/t) that can be determined analytically. Let ρ 0 be the initial density matrix for the two disconnected chains then [25] …”

Section: C2 Semiclassical Limitmentioning

confidence: 99%

“…when the two halves are held at different temperatures T l and T r . The large x and t behavior is still dominated by the pole in f (k, q) [25] with residue proportional to the Fermi-Dirac distributions at temperatures T l/r . The inhomogeneous energy density profile can be similarly computed [22].…”

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Inhomogeneous quenches in a free fermionic chain: Exact results

Viti¹,

Stéphan²,

Dubail³

et al. 2016

EPL

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We consider the non-equilibrium physics induced by joining together two tight binding fermionic chains to form a single chain. Before being joined, each chain is in a many-fermion ground state. The fillings (densities) in the two chains might be the same or different. We present a number of exact results for the correlation functions in the non-interacting case. We present a short-time expansion, which can sometimes be fully resummed, and which reproduces the so-called 'light cone' effect or wavefront behavior of the correlators. For large times, we show how all interesting physical regimes may be obtained by stationary phase approximation techniques. In particular, we derive semiclassical formulas in the case when both time and positions are large, and show that these are exact in the thermodynamic limit. We present subleading corrections to the large-time behavior, including the corrections near the edges of the wavefront. We also provide results for the return probability or Loschmidt echo. In the maximally inhomogeneous limit, we prove that it is exactly gaussian at all times. The effects of interactions on the Loschmidt echo are also discussed.PACS numbers: 75.10. Fd, 75.45.Gm, 05.60.Gg Introduction -Local quantum quenches are a particularly neat setup to address theoretical questions about non-equilibrium current-carrying stationary states as well as transport properties of many-body isolated quantum systems. The characterization of the long-time behavior of local correlation functions unveils universal features of the quantum dynamics [1][2][3][4][5] and paves the way to the construction of effective field theories capable of capturing them. Analytic results are relevant as benchmarks for cold atom experiments that very recently [6][7][8] started to investigate particle and energy transport under a unitary dynamics.In this work, we study a quench which, although injecting an extensive amount of energy into the system, has mostly local effects. We take two uniformly filled long tight binding chains in their respective ground-states, but with a different number of fermions. At time t = 0 the two edges are connected so that it turns into a single chainThe hopping and interactions between sites j = 0 and j = 1 are initially absent; the initial state |ψ 0 = |ψ l |ψ r is the tensor product of the ground states (with specified occupancies) of the two decoupled chains. For unequal fillings, one expects some particle current at time t > 0. We denote by k l F (k r F ) the Fermi momenta on the left (right), so that the particle number is2 ) on the left (right). For simplicity we focus on the symmetric case k l F + k r F = π, but extension to other values is straightforward. It is useful to keep two limits in mind. When the fillings are equal k l F = k r F = π/2 there is no particle current. This particular quench was studied in [1][2][3]9], using low-energy field theory, and belongs to the class of Fermi-edge problems [10,11]. The other simple limit is k The motivation for the present study is two-fold. First, ou...

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Stationary states in a free fermionic chain from the quench action method

Cited by 65 publications

References 53 publications

Black brane steady states

Black brane steady states

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

Inhomogeneous quenches in a free fermionic chain: Exact results

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