Simulating continuous symmetry models with discrete ones

Abstract

Especially in one dimension, models with discrete and continuous symmetries display different physical properties, starting from the existence of long-range order. In this work, we that, by adding topological frustration, an antiferromagnetic $XYZ$ spin chain, characterized by a discrete local symmetry, develops a region in parameter space which mimics the features of models with continuous symmetries. For instance, frustration closes the mass gap and we describe a continuous crossover between ground states with different quantum numbers, a finite (Fermi) momentum for low energy states, and the disappearance of the finite order parameter. Moreover, we observe non-trivial ground state degeneracies, non-vanishing chirality and a singular foliation of the ground state fidelity . Across the boundary between this chiral region and the rest of the phase diagram any discontinuity in the energy derivatives vanishes in the thermodynamic limit.

References in corpus (6)

• Quantum critical scaling of the geometric tensors
• The quantum adiabatic algorithm and scaling of gaps at first order quantum phase transitions
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Reduced fidelity susceptibility and its finite-size scaling behaviors
• Exploring chaos in Dicke Model using ground state fidelity and Loschmidt echo
• Partial-state fidelity and quantum phase transitions induced by continuous level crossing

Cited by in corpus (9)

• Frustrating quantum batteries
• Magic phase transition and non-local complexity in generalized $W$ State
• Towards a phase diagram of the topologically frustrated XY chain
• Random unitaries, Robustness, and Complexity of Entanglement
• Interplay between local and non-local frustration in the 1D ANNNI chain I -- The even case
• The quantum XY chain with boundary fields: finite-size gap and phase behavior
• Few-body precursors of topological frustration
• Anisotropy-induced spin parity effects
• Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors