Entanglement evolution after connecting finite to infinite quantum chains

Abstract:We propose a holographic model for local quench in 1 + 1 dimensional Conformal Field Theory (CFT). The local quench is produced by joining two identical CFT's on semi-infinite lines. When these theories have a zero boundary entropy, we use the AdS/Boundary CFT proposal to describe this process in terms of bulk physics. Boundaries of the original CFT's are extended in AdS as dynamical surfaces. In our holographic picture these surfaces detach from the boundary and form a closed folded string which can propagate in the bulk. The dynamics of this string is governed by the tensionless Yo-Yo string solution and its subsequent evolution determines the time dependence after quench. We use this model to calculate holographic Entanglement Entropy (EE) of an interval as a function of time. We propose how the falling string deforms Ryu-Takayanagi's curves. Using the deformed curves we calculate EE and find complete agreement with field theory results.

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“…where 9) and since x = 0 when z = 0, we should set β = 0. The situation has been schematically shown in figure 1.…”

Section: Ads/bcft Correspondencementioning

confidence: 99%

“…This process is called Local Quench and the question of interest is the time evolution of the system after quench [8,9] and [10].…”

Section: Introductionmentioning

confidence: 99%

Quantum local quench, AdS/BCFT and Yo-Yo string

Astaneh

Mosaffa

2015

J. High Energ. Phys.

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“…Like in the more complicated case of the "swap" quench, one can be interested in measuring the overlap between the two ground states of H and H . Let us refer to this local quench as the "cut-and-glue" quench; it is a problem that has been studied in recent papers [56,55,15,32]. Let us emphasize that the overlap between the two ground states H and H is not a Rényi entropy like in the case of the "swap" quench.…”

Section: Appendix A2 Action Of the Swap Operator On A Local Hamiltomentioning

confidence: 99%

Logarithmic corrections to the free energy from sharp corners with angle 2π

Stéphan¹,

Dubail²

2013

J. Stat. Mech.

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Abstract. We study subleading corrections to the corner free energy in classical two-dimensional critical systems, focusing on a generic boundary perturbation by the stress-tensor of the underlying conformal field theory (CFT). In the particular case of an angle 2π, we find that there is an unusual correction of the form L −1 log L, where L is a typical length scale in the system. This correction also affects the one-point function of an operator near the corner. The prefactor can be seen as semi-universal, in the sense that it depends on a single non-universal quantity, the extrapolation length. Once this ultraviolet cutoff is known, the term is entirely fixed by the geometry of the system, and the central charge of the CFT. Such a corner appears for example in the bipartite fidelity of a one-dimensional quantum system at criticality, which allows for several numerical checks in free fermions systems. We also present an exact result in the XX and Ising chains that confirms this analysis. Finally, we consider applications to the time evolution of the (logarithmic) Loschmidt echo and the entanglement entropy following a local quantum quench. Due to subtle issues in analytic continuation, we find that the logarithmic term in imaginary time transforms into a time-dependent L −2 correction for the entanglement entropy, and a L −2 log L term for the Loschmidt echo.

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“…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 l F = π, with a domain wall (DW) initial state [12][13][14] |ψ 0 = x≤0 c † x |0 , where |0 is the fermion vacuum.…”

mentioning

confidence: 99%

Inhomogeneous quenches in a free fermionic chain: Exact results

Viti¹,

Stéphan²,

Dubail³

et al. 2016

EPL

114

189

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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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Entanglement evolution after connecting finite to infinite quantum chains

Cited by 80 publications

References 25 publications

Quantum local quench, AdS/BCFT and Yo-Yo string

Quantum local quench, AdS/BCFT and Yo-Yo string

Logarithmic corrections to the free energy from sharp corners with angle 2π

Inhomogeneous quenches in a free fermionic chain: Exact results

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