Related papers: Entanglement asymmetry in CFT and its relation to non-topological defects

Entanglement asymmetry in CFT and its relation to non-topological defects

URL: http://arxiv.org/abs/2402.03446v1
Date: Mon, 5 Feb 2024 19:01:09 GMT
Title: Entanglement asymmetry in CFT and its relation to non-topological defects
Authors: Michele Fossati, Filiberto Ares, Jerome Dubail, Pasquale Calabrese
Abstract summary: The entanglement asymmetry is an information based observable that quantifies the degree of symmetry breaking in a region of an extended quantum system. We investigate this measure in the ground state of one dimensional critical systems described by a CFT.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The entanglement asymmetry is an information based observable that quantifies the degree of symmetry breaking in a region of an extended quantum system. We investigate this measure in the ground state of one dimensional critical systems described by a CFT. Employing the correspondence between global symmetries and defects, the analysis of the entanglement asymmetry can be formulated in terms of partition functions on Riemann surfaces with multiple non-topological defect lines inserted at their branch cuts. For large subsystems, these partition functions are determined by the scaling dimension of the defects. This leads to our first main observation: at criticality, the entanglement asymmetry acquires a subleading contribution scaling as $\log \ell / \ell$ for large subsystem length $\ell$. Then, as an illustrative example, we consider the XY spin chain, which has a critical line described by the massless Majorana fermion theory and explicitly breaks the $U(1)$ symmetry associated with rotations about the $z$-axis. In this situation the corresponding defect is marginal. Leveraging conformal invariance, we relate the scaling dimension of these defects to the ground state energy of the massless Majorana fermion on a circle with equally-spaced point defects. We exploit this mapping to derive our second main result: the exact expression for the scaling dimension associated with $n$ of defects of arbitrary strengths. Our result generalizes a known formula for the $n=1$ case derived in several previous works. We then use this exact scaling dimension to derive our third main result: the exact prefactor of the $\log \ell/\ell$ term in the asymmetry of the critical XY chain.

Related papers

Entanglement asymmetry in the critical XXZ spin chain [0.0]
We study the explicit breaking of a $SU(2)$ symmetry to a $U(1)$ subgroup employing the entanglement asymmetry. We consider as specific model the critical XXZ spin chain, which breaks the $SU(2)$ symmetry of spin rotations except at the isotropic point.
arXiv Detail & Related papers (2024-07-08T22:16:22Z)
Universal non-Hermitian flow in one-dimensional PT-symmetric quantum criticalities [5.402334522977581]
We study the finite-size scaling of the energy of non-Hermitian Su-Schrieffer-Heeger model with parity and time-reversal symmetry. We find that under open boundary condition (OBC), the energy scaling $E(L)sim c/L$ reveals a negative central charge $c=-2$ at the non-Hermitian critical point. The scaling function demonstrates distinct behaviors at topologically non-trivial and trivial sides of critical points.
arXiv Detail & Related papers (2024-05-02T18:02:13Z)
Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
arXiv Detail & Related papers (2024-04-04T14:45:28Z)
Symmetry-resolved Entanglement Entropy, Spectra & Boundary Conformal Field Theory [0.0]
We perform a comprehensive analysis of the symmetry-resolved entanglement entropy (EE) for one single interval in the ground state of a $1+1$D conformal field theory (CFT) We utilize the boundary CFT approach to study the total EE, which enables us to find the universal leading order behavior of the SREE. We derive the symmetry-resolved entanglement spectra for a CFT invariant under a finite symmetry group.
arXiv Detail & Related papers (2023-09-06T18:03:14Z)
Entanglement phase transition due to reciprocity breaking without measurement or post-selection [59.63862802533879]
EPT occurs for a system undergoing purely unitary evolution. We analytically derive the entanglement entropy out of and at the critical point for the $l=1$ and $l/N ll 1$ case.
arXiv Detail & Related papers (2023-08-28T14:28:59Z)
Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
arXiv Detail & Related papers (2023-05-11T15:57:27Z)
Theory of free fermions under random projective measurements [43.04146484262759]
We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
arXiv Detail & Related papers (2023-04-06T15:19:33Z)
Symmetry-resolved entanglement in critical non-Hermitian systems [0.0]
We study the symmetry-resolved entanglement in the ground state of the non-Hermitian Su-Schrieffer-Heeger chain at the critical point. By combining bosonization techniques in the field theory and exact lattice numerical calculations, we analytically derive the charged moments of $rho_A$ and $|rho_A|$.
arXiv Detail & Related papers (2023-03-09T13:14:26Z)
Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
arXiv Detail & Related papers (2021-07-20T18:44:06Z)
Entanglement Entropy of Non-Hermitian Free Fermions [59.54862183456067]
We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems.
arXiv Detail & Related papers (2021-05-20T14:46:09Z)
Finite-size corrections in critical symmetry-resolved entanglement [0.0]
We show that the nature of the symmetry group plays a crucial role in symmetry-resolved entanglement entropies. In the case of a discrete symmetry group, the corrections decay algebraically with system size, with exponents related to the operators' scaling dimensions. In contrast, in the case of a U(1) symmetry group, the corrections only decay logarithmically with system size, with model-dependent prefactors.
arXiv Detail & Related papers (2020-10-20T12:18:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.