Quantum phase transitions about parity breaking in matrix product systems

Abstract

According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.

Quantum phase transitions in composite matrix product states of one-dimensional spin-1/2 chains

“…[1][2][3][4] Hence MPSs is an undoubtedly convenient platform for studying novel kinds of quantum phase transitions. 1,[5][6][7][8][9][10][11][12][13] For one-dimensional spin-1 chains, based on the space reversal properties of MPSs, we investigated quantum phase transitions between subsystems of two-subsystem composite MPSs. 12,13 In this paper, we make the precondition the space reversal properties of MPSs be more in general and investigate a novel kind of quantum phase transition of a composite MPS of onedimensional spin-1/2 chain to see what novel properties there are.…”

Critical behavior of the XY spin chain with three-site interaction studied in terms of the Loschmidt echo

“…Zanardi and Paunkovic characterized QPT in terms of the overlap function between two ground states obtained from two different external parameter values [6]. Additionally, fidelity or fidelity susceptibility (FS) [7][8][9], pair-wise quantum discord [10], the Berry phase [11,12], the matrix product state [13] and the photon bunching effect [14] have also shown a close relationship with QPT.…”