Spontaneous symmetry breaking and bifurcations in ground state fidelity for quantum lattice systems

Abstract

Spontaneous symmetry breaking occurs in a system when its Hamiltonian possesses a certain symmetry, whereas the ground state wave functions do not preserve it. This provides such a scenario that a bifurcation, which breaks the symmetry, occurs when some control parameter crosses its critical value. It is unveiled that the ground state fidelity per lattice site exhibits such a bifurcation for quantum lattice systems undergoing quantum phase transitions. The significance of this result lies in the fact that the ground state fidelity per lattice site is \textit{universal}, in the sense that it is model-independent, in contrast to (model-dependent) order parameters. This fundamental quantity may be computed by exploiting the newly-developed tensor network algorithms on infinite-size lattices. We illustrate the scheme in terms of the quantum Ising model in a transverse magnetic field and the spin 1/2 XYX model in an external magnetic field on an infinite-size lattice in one spatial dimension.

4+pages, 3 figures

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Cited by in corpus (15)

• Geometry of quantum phase transitions
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Matrix Product State and Quantum Phase Transitions in the One-Dimensional Extended Quantum Compass Model
• Non-local correlations in the Haldane phase for an XXZ spin-1 chain: A perspective from infinite matrix product state representation
• Quantum fidelity for degenerate groundstates in quantum phase transitions
• Stability of the Trotter-Suzuki decomposition
• Degenerate groundstates and multiple bifurcations in a two-dimensional q-state quantum Potts model
• Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
• Fidelity and entanglement entropy for infinite-order phase transitions
• Ground state fidelity in bond-alternative Ising chains with Dzyaloshinskii-Moriya interactions
• The antiferromagnetic cross-coupled spin ladder: quantum fidelity and tensor networks approach
• Geometric entanglement from matrix product state representations
• Bifurcation in ground-state fidelity for a one-dimensional spin model with competing two-spin and three-spin interactions
• Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach
• Groundstate fidelity phase diagram of the fully anisotropic two-leg spin-1/2 XXZ ladder