Entanglement of excited states in critical spin chains

Ibáñez-Berganza, Miguel; Alcaraz, Francisco C.; Sierra, Germȧn

doi:10.1088/1742-5468/2012/01/p01016

Cited by 74 publications

(97 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We focus on those aspects that will be useful to the present paper, more general details can be found in, e.g., Refs. [9,[45][46][47][48][49][50] and references therein.…”

Section: Local Operator Quenches In Spin Chainsmentioning

confidence: 99%

Subsystem distance after a local operator quench

Zhang

Calabrese

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

We investigate the time evolution of the subsystem trace distance and Schatten distances after local operator quenches in two-dimensional conformal field theory (CFT) and in one-dimensional quantum spin chains. We focus on the case of a subsystem being an interval embedded in the infinite line. The initial state is prepared by inserting a local operator in the ground state of the theory. We only consider the cases in which the inserted local operator is a primary field or a sum of several primaries. While a nonchiral primary operator can excite both left-moving and rightmoving quasiparticles, a holomorphic primary operator only excites a right-moving quasiparticle and an anti-holomorphic primary operator only excites a left-moving one. The reduced density matrix (RDM) of an interval hosting a quasiparticle is orthogonal to the RDM of the interval without any quasiparticles. Moreover, the RDMs of two intervals hosting quasiparticles at different positions are also orthogonal to each other. We calculate numerically the entanglement entropy, Rényi entropy, trace distance, and Schatten distances in time-dependent states excited by different local operators in the critical Ising and XX spin chains. These results match the CFT predictions in the proper limit.

show abstract

“…We focus on those aspects that will be useful to the present paper, more general details can be found in, e.g., Refs. [9,[45][46][47][48][49][50] and references therein.…”

Section: Local Operator Quenches In Spin Chainsmentioning

confidence: 99%

Subsystem distance after a local operator quench

Zhang

Calabrese

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…Then trρ n X is given by n copies of the RDM ρ X sewed cyclically along A. Following this standard procedure, we end up in a world-sheet which is the n-sheeted Riemann surface R n , and the moments of ρ X are [75,76]…”

Section: Short Interval Expansionmentioning

confidence: 99%

“…In the case of A being a single interval, in order to calculate the correlators appearing in (2.15), one could either introduce twist fields (as mentioned above) or consider a conformal transformation mapping the Riemann surface to the complex plane, where the correlators themselves can be explicitly evaluated. While the representation in terms of twist field is a powerful tool to get the short-interval expansion, this second method allows in some cases to get the full analytic result for an interval of arbitrary length, at least in the case when X is a primary field and the mapping to the complex plane has no anomalous terms [75,76]. The above results have been generalised in the literature to many other situations, e.g., states generated by descendant fields [77,78], boundary theories [79,80], and systems with disorder [81].…”

Section: Short Interval Expansionmentioning

confidence: 99%

See 1 more Smart Citation

Subsystem trace distance in low-lying states of (1 + 1)-dimensional conformal field theories

Zhang

Ruggiero

Calabrese

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

We report on a systematic replica approach to calculate the subsystem trace distance for a quantum field theory. This method has been recently introduced in [J. Zhang, P. Ruggiero, P. Calabrese, Phys. Rev. Lett. 122, 141602 (2019)], of which this work is a completion. The trace distance between two reduced density matrices ρ A and σ A is obtained from the moments tr(ρ A −σ A ) n and taking the limit n → 1 of the traces of the even powers. We focus here on the case of a subsystem consisting of a single interval of length embedded in the low lying eigenstates of a one-dimensional critical system of length L, a situation that can be studied exploiting the path integral form of the reduced density matrices of two-dimensional conformal field theories. The trace distance turns out to be a scale invariant universal function of /L. Here we complete our previous work by providing detailed derivations of all results and further new formulas for the distances between several lowlying states in two-dimensional free massless compact boson and fermion theories. Remarkably, for one special case in the bosonic theory and for another in the fermionic one, we obtain the exact trace distance, as well as the Schatten n-distance, for an interval of arbitrary length, while in generic case we have a general form for the first term in the expansion in powers of /L. The analytical predictions in conformal field theories are tested against exact numerical calculations in XX and Ising spin chains, finding perfect agreement. As a byproduct, new results in two-dimensional CFT are also obtained for other entanglement-related quantities, such as the relative entropy and the fidelity.

show abstract

“…The bipartite entanglement entropy of the excited states in the quantum spin chains was first studied with exact methods in [28], see also [29]. Then the entanglement entropy of the low-lying excited states in CFTs was calculated in [30,31]. For recent numerical calculations regarding the entanglement entropy of the excited states in the quantum spin chains and free fermions see [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47].…”

mentioning

confidence: 99%

Bipartite entanglement entropy of the excited states of free fermions and harmonic oscillators

Jafarizadeh

Rajabpour

2019

Phys. Rev. B

View full text Add to dashboard Cite

We study general entanglement properties of the excited states of the one dimensional translational invariant free fermions and coupled harmonic oscillators. In particular, using the integrals of motion, we prove that these Hamiltonians independent of the gap (mass) has infinite excited states that can be described by conformal field theories with integer or half-integer central charges. In the case of free fermions, we also show that because of the huge degeneracy in the spectrum, even a gapless Hamiltonian can have excited states with an area-law. Finally, we study the universal average entanglement entropy over eigenstates of the Hamiltonian of the free fermions introduced recently in [L. Vidmar, et al., Phys. Rev. Lett. 119, 020601 (2017)]. In particular, using a duality relation, we propose a method which can be useful for experimental measurement of the universal average entanglement entropy. Part of our conclusions can be extended to the quantum spin chains that are associated with the free fermions via Jordan-Wigner(JW) transformation.

show abstract

Entanglement of excited states in critical spin chains

Cited by 74 publications

References 37 publications

Subsystem distance after a local operator quench

Subsystem distance after a local operator quench

Subsystem trace distance in low-lying states of (1 + 1)-dimensional conformal field theories

Bipartite entanglement entropy of the excited states of free fermions and harmonic oscillators

Contact Info

Product

Resources

About