Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains

Arias, Raúl; Zhang, Jiaju

doi:10.1088/1742-5468/ababfd

Cited by 9 publications

(4 citation statements)

References 100 publications

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“…In quantum information theory, it is often important to know the quantitative difference between two density matrices, especially for two subsystem RDMs. The subsystem distance has been studied in various circumstances, see for example [51][52][53][54][55][56][57][58][59][60][61]. There are many definitions of the distance between two density matrices [62][63][64].…”

Section: Jhep08(2021)106mentioning

confidence: 99%

“…For general excited states, we will calculate the leading order of the short interval expansion of the Rényi entropy using twist operators [21,26,66] and their operator product expansion (OPE) [67][68][69][70]. Similarly, we will calculate the exact value [54,56] and short interval expansion [52,53,61] of the Schatten distance in the 2D massless bosonic theory. In the locally coupled harmonic chain, we will use the wave function method [41,42] to calculate numerically the Rényi entropy and subsystem Schatten distance.…”

Section: Jhep08(2021)106mentioning

confidence: 99%

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

Zhang

Rajabpour

2021

J. High Energ. Phys.

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We study the excited state Rényi entropy and subsystem Schatten distance in the two-dimensional free massless non-compact bosonic field theory, which is a conformal field theory. The discretization of the free non-compact bosonic theory gives the harmonic chain with local couplings. We consider the field theory excited states that correspond to the harmonic chain states with excitations of more than one quasiparticle, which we call multi-particle states. This extends the previous work by the same authors to more general excited states. In the field theory we obtain the exact Rényi entropy and subsystem Schatten distance for several low-lying states. We obtain short interval expansion of the Rényi entropy and subsystem Schatten distance for general excited states, which display different universal scaling behaviors in the gapless and extremely gapped limits of the non-compact bosonic theory. In the locally coupled harmonic chain we calculate numerically the excited state Rényi entropy and subsystem Schatten distance using the wave function method. We find excellent matches of the analytical results in the field theory and numerical results in the gapless limit of the harmonic chain. We also make some preliminary investigations of the Rényi entropy and the subsystem Schatten distance in the extremely gapped limit of the harmonic chain.

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Section: Jhep08(2021)106mentioning

confidence: 99%

Section: Jhep08(2021)106mentioning

confidence: 99%

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

Zhang

Rajabpour

2021

J. High Energ. Phys.

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“…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]. There are many definitions of the distance between two states, see for example [86][87][88].…”

Section: S (N)mentioning

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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“…[38,[61][62][63][64][65]. Also the Schatten distances have been studied in field theories [37,38,[65][66][67][68][69], but not as much as the relative entropy, most likely because of the more difficult replica approach (see below) necessary for their determination.…”

Section: Introductionmentioning

confidence: 99%

Symmetry resolved relative entropies and distances in conformal field theory

Capizzi,

Calabrese

2021

Preprint

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We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory having an internal U(1) symmetry. We provide analytic expressions for the charged moments corresponding to the resolution of both relative entropies and distances for general integer n. For the relative entropies, these formulas are manageable and the analytic continuation to n = 1 can be worked out in most of the cases. Conversely, for the distances the corresponding charged moments become soon untreatable as n increases. A remarkable result is that relative entropies and distances are the same for all symmetry sectors, i.e. they satisfy entanglement equipartition, like the entropies. Moreover, we exploit the OPE expansion of composite twist fields, to provide very general results when the subsystem is much smaller than the total system. We focus on the massless compact boson and our results are tested against exact numerical calculations in the XX spin chain.

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Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains

Cited by 9 publications

References 100 publications

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

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

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

Symmetry resolved relative entropies and distances in conformal field theory

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