Subsystem distance after a local operator quench

Zhang, Jiaju; Calabrese, Pasquale

doi:10.1007/jhep02(2020)056

Cited by 25 publications

(26 citation statements)

References 83 publications

(143 reference statements)

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“…This is in agreement with the known metric properties of the trace distance (see, e.g., Ref. [47,48]); it also confirms some observations done for excited states of CFTs [49,50], as well as out of equilibrium [51].…”

Section: Trace Distance and Its Propertiessupporting

confidence: 92%

Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

et al. 2020

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We carry out a comprehensive comparison between the exact modular Hamiltonian and the lattice version of the Bisognano-Wichmann (BW) one in one-dimensional critical quantum spin chains. As a warm-up, we first illustrate how the trace distance provides a more informative mean of comparison between reduced density matrices when compared to any other Schatten nn-distance, normalized or not. In particular, as noticed in earlier works, it provides a way to bound other correlation functions in a precise manner, i.e., providing both lower and upper bounds. Additionally, we show that two close reduced density matrices, i.e. with zero trace distance for large sizes, can have very different modular Hamiltonians. This means that, in terms of describing how two states are close to each other, it is more informative to compare their reduced density matrices rather than the corresponding modular Hamiltonians. After setting this framework, we consider the ground states for infinite and periodic XX spin chain and critical Ising chain. We provide robust numerical evidence that the trace distance between the lattice BW reduced density matrix and the exact one goes to zero as \ell^{-2}ℓ−2 for large length of the interval \ellℓ. This provides strong constraints on the difference between the corresponding entanglement entropies and correlation functions. Our results indicate that discretized BW reduced density matrices reproduce exact entanglement entropies and correlation functions of local operators in the limit of large subsystem sizes. Finally, we show that the BW reduced density matrices fall short of reproducing the exact behavior of the logarithmic emptiness formation probability in the ground state of the XX spin chain.

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Section: Trace Distance and Its Propertiessupporting

confidence: 92%

Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

et al. 2020

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“…Moreover, this is also a simple generalization of the result in Ref. [25], where the superposition of purely holomorphic and anti-holomorphic primaries was considered.…”

Section: Fermionic Excitationsupporting

confidence: 63%

“…Despite this increased attention, there have been much less studies on entanglement spreading after local excitations in integrable quantum chains. The CFT predictions have been tested on the critical transverse Ising [24] and XX chains [25], for various local operators that are lattice analogs of primary or descendant fields. On the other hand, entanglement spreading has also been considered in the non-critical ordered phase of the Ising [26] and XY chains [27,28], starting from a domain-wall initial state excited by a local Majorana operator.…”

Section: Introductionmentioning

confidence: 99%

Entanglement spreading after local fermionic excitations in the XXZ chain

Gruber

Eisler

2021

SciPost Phys.

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We study the spreading of entanglement produced by the time evolution of a local fermionic excitation created above the ground state of the XXZ chain. The resulting entropy profiles are investigated via density-matrix renormalization group calculations, and compared to a quasiparticle ansatz. In particular, we assume that the entanglement is dominantly carried by spinon excitations traveling at different velocities, and the entropy profile is reproduced by a probabilistic expression involving the density fraction of the spinons reaching the subsystem. The ansatz works well in the gapless phase for moderate values of the XXZ anisotropy, eventually deteriorating as other types of quasiparticle excitations gain spectral weight. Furthermore, if the initial state is excited by a local Majorana fermion, we observe a nontrivial rescaling of the entropy profiles. This effect is further investigated in a conformal field theory framework, carrying out calculations for the Luttinger liquid theory. Finally, we also consider excitations creating an antiferromagnetic domain wall in the gapped phase of the chain, and find again a modified quasiparticle ansatz with a multiplicative factor.

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“…In [77,78] the subsystem distance was used to quantify the precision of the approximate entanglement Hamiltonian coming from the discretization of the Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains [79,80]. The subsystem distance was also used in [81] to characterize the local operator quench in 2D CFTs and spin chains [82][83][84]. Recently, the subsystem distance in the thermal states of the finite size critical XY chains was investigated in [85].…”

Section: S (N)mentioning

confidence: 99%

“…The 2D free massless non-compact bosonic theory, which is a 2D CFT with the central charge c = 1, is the continuum limit of the gapless harmonic chain with the local couplings (2.3). We follow mainly [81], however one can also see [89][90][91][92][93] for more rigorous identifications of the states and operators in the 2D CFTs and critical lattices. One can consult [94,95] for the basics of the 2D free massless bosonic theory.…”

Section: Identification Of Cft and Harmonic Chain Statesmentioning

confidence: 99%

Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

Zhang

Rajabpour

2020

J. High Energ. Phys.

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We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

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Subsystem distance after a local operator quench

Cited by 25 publications

References 83 publications

Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains

Entanglement spreading after local fermionic excitations in the XXZ chain

Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

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