Logarithmic current fluctuations in nonequilibrium quantum spin chains

Antal, Tibor; Krapivsky, P. L.; Rákos, A.

doi:10.1103/physreve.78.061115

Cited by 87 publications

(159 citation statements)

References 45 publications

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“…Note that (19) can also be written as C ′ (t)(1 − C ′ (t)) = λ 2 C(t)(1 − C(t)) and is then identical to the relation for the overlap matrix A in a (static) continuum system [6][7][8]. The problem is now reduced to that of the homogeneous quench, but one still needs the ε l (t).…”

Section: Quench From Equal Fillingsmentioning

confidence: 99%

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On entanglement evolution across defects in critical chains

Eisler

Peschel

2012

EPL

103

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Section: Quench From Equal Fillingsmentioning

confidence: 99%

“…In the homogeneous case, the time evolution of the density profile [18], the particle number fluctuations in a half-chain [19] as well as the entanglement entropy [20] have been studied previously. The fluctuations and the entropy both grow logarithmically in time.…”

Section: Quench From Unequal Fillingsmentioning

confidence: 99%

On entanglement evolution across defects in critical chains

Eisler

Peschel

2012

EPL

103

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“…The equilibrium magnetization can be computed by evaluating the matrix element in (9). Rewriting σ x n with Majorana operators one has…”

Section: Model and Settingmentioning

confidence: 99%

“…Under time evolution the initial inhomogeneity spreads ballistically, creating a front region which grows linearly in time. While the overall shape of the front is simple to obtain from a hydrodynamic (semiclassical) picture in terms of the fermionic excitations [9], the fine structure is more involved and shows universal features around the edge of the front [10,11] The melting of domain walls has been considered in various different lattice models, such as the transverse Ising [12,13], the XY [14] and XXZ chains [15][16][17][18], hard-core bosons [19][20][21], as well as in the continuum for a Luttinger model [22], the Lieb-Liniger gas [23] or within conformal field theory [24,25]. Instead of a sharp domain wall, the melting of inhomogeneous interfaces can also be studied by applying a magnetic field gradient, which is then suddenly quenched to zero [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Universal front propagation in the quantum Ising chain with domain-wall initial states

2016

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We study the melting of domain walls in the ferromagnetic phase of the transverse Ising chain, created by flipping the order-parameter spins along one-half of the chain. If the initial state is excited by a local operator in terms of Jordan-Wigner fermions, the resulting longitudinal magnetization profiles have a universal character. Namely, after proper rescalings, the profiles in the noncritical Ising chain become identical to those obtained for a critical free-fermion chain starting from a step-like initial state. The relation holds exactly in the entire ferromagnetic phase of the Ising chain and can even be extended to the zero-field XY model by a duality argument. In contrast, for domain-wall excitations that are highly non-local in the fermionic variables, the universality of the magnetization profiles is lost. Nevertheless, for both cases we observe that the entanglement entropy asymptotically saturates at the ground-state value, suggesting a simple form of the steady state.

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“…The large-time behavior for fixed x and y is then determined [21] from the points where the phase is stationary, as well as possible singularities in f (k, q). For this type of protocol, it is for example known that a NESS develops in the middle [14][15][16]. Here we are interested in a different regime at large time where x/t is kept finite.…”

mentioning

confidence: 99%

Inhomogeneous quenches in a free fermionic chain: Exact results

Viti¹,

Stéphan²,

Dubail³

et al. 2016

EPL

114

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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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Logarithmic current fluctuations in nonequilibrium quantum spin chains

Cited by 87 publications

References 45 publications

On entanglement evolution across defects in critical chains

On entanglement evolution across defects in critical chains

Universal front propagation in the quantum Ising chain with domain-wall initial states

Inhomogeneous quenches in a free fermionic chain: Exact results

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