Ground state entanglement in quantum spin chains

Abstract

A microscopic calculation of ground state entanglement for the XY and Heisenberg models shows the emergence of universal scaling behavior at quantum phase transitions. Entanglement is thus controlled by conformal symmetry. Away from the critical point, entanglement gets saturated by a mass scale. Results borrowed from conformal field theory imply irreversibility of entanglement loss along renormalization group trajectories. Entanglement does not saturate in higher dimensions which appears to limit the success of the density matrix renormalization group technique. A possible connection between majorization and renormalization group irreversibility emerges from our numerical analysis.

Pseudo-Entropy in Free Quantum Field Theories

“…Very similar to the case of the reduced density matrix in calculation of the von Neumann entropy, introduced in [6], the spectrum of this iΓ matrix is related to a double copy of the spectrum of the transition matrix as…”

“…To adapt the correlator method for calculation of pseudo entropy corresponding to a single block of spins in these models, we consider the fermionic representation (see for instance [6] for the details of the Jordan-Wigner transformation) of the XY chain as…”

“…As one of the most fundamental quantum resources, entanglement plays key roles in almost all areas of quantum physics, not only practically but also theoretically. One branch is its application to quantum many body systems, which has revealed many important properties of correlation structures [2][3][4][5], quantum phase transitions [3,6], thermalization process [7,8] and emergence of spacetime [9][10][11][12]. Entanglement entropy is the most often used quantity to measure the amount of entanglement between two parts of a quantum system.…”

Scaling of variational quantum circuit depth for condensed matter systems

“…where c is the central charge of the corresponding CFT and d is a non-universal constant [45][46][47][48]. In the case of conformally invariant gapless Hamiltonian, we thus expect that the number of layers of our ansatz in Fig.…”

The density-matrix renormalization group: a short introduction

“…in one dimension and S ∼ L in two dimensions. At criticality, a much richer structure emerges, which usually involves the presence or absence of logarithmic corrections (S (L) ∝ log L, S (L) ∝ L log L in one dimension and two dimensions), see Srednicki [20], Vidal et al [24], Latorre et al [25], Gioev & Klich [26] and Barthel et al [27]. It should be emphasized that these properties of ground states are highly unusual: in the thermodynamic limit, a random state out of Hilbert space will indeed show extensive entanglement entropy with probability 1.…”