Entanglement entropy scaling of the XXZ chain

Abstract

Abstract. We study the entanglement entropy scaling of the XXZ chain. While in the critical XY phase of the XXZ chain the entanglement entropy scales logarithmically with a coefficient that is determined by the associated conformal field theory, at the ferromagnetic point, however, the system is not conformally invariant yet the entanglement entropy still scales logarithmically albeit with a different coefficient. We investigate how such an nontrivial scaling at the ferromagnetic point influences the estimation of the central charge c in the critical XY phase. In particular we use the entanglement scaling of the finite or infinite system, as well as the finite-size scaling of the ground state energy to estimate the value of c. In addition, the spin-wave velocity and the scaling dimension are also estimated. We show that in all methods the evaluations are influenced by the nearby ferromagnetic point and result in crossover behavior. Finally we discuss how to determine whether the central charge estimation is strongly influenced by the crossover behavior and how to properly evaluate the central charge.Entanglement entropy scaling of the XXZ chain 2

Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain

“…[38], by studying the renormalization group flow of the NH sine-Gordon model, it is pointed out that the model for large |g 3 | is governed by the strong-coupling fixed point, where the cosine term in the NH sine-Gordon model becomes relevant. As the finite-size effect is known to become significant when the system approaches the transition point [110,111], the renormalization group analysis is consistent with our NH-DMRG calculation.…”

“…3(c) and (d), the results obtained by NH-DMRG (solid lines) agree well with the exact solutions (dotted lines) for small |∆ γ |. Though their discrepancy becomes singnificant for large |∆ γ |, these features have also been reported in Hermitian cases [110,111]. This is because the finite-size effect becomes significant as the model approaches the transition point, at which the cosine term of the NH sine-Gordon model (9) becomes relevant.…”

Entanglement structure of a quantum simulator: the two-component Bose-Hubbard model

“…( 6) an asymptotic expression for the von Neumann entropy S E can be obtained considering l = L/2 and S z T = 0 Notice that in the thermodynamic limit any small anisotropy D > 0 will restore the conformal symmetry. For finite systems a smooth crossover between the CFT and the scale invariant prediction ( 7) is expected 24 , see inset Fig. 2.…”

Entanglement structure of the two-component Bose-Hubbard model as a quantum simulator of a Heisenberg chain

“…Notice that in the thermodynamic limit any small anisotropy D > 0 will restore the conformal symmetry. For finite systems a smooth crossover between the CFT and the scale invariant prediction (8) is expected 28 , see Fig. 2.…”