Strong and weak symmetries and their spontaneous symmetry breaking in mixed states emerging from the quantum Ising model under multiple decoherence

Abstract

Discovering and categorizing quantum orders in mixed many-body systems are currently one of the most important problems. Specific types of decoherence applied to typical quantum many-body states can induce a novel kind of mixed state accompanying characteristic symmetry orders, which has no counterparts in pure many-body states. We study phenomena generated by interplay between two types of decoherence applied to the one-dimensional transverse field Ising model (TFIM). We show that in the doubled Hilbert space formalism, the decoherence can be described by filtering operation applied to matrix product states (MPS) defined in the doubled Hilbert system. The filtering operation induces specific deformation of the MPS, which approximates the ground state of a certain parent Hamiltonian in the doubled Hilbert space. In the present case, such a parent Hamiltonian is the quantum Ashkin-Teller model, having a rich phase diagram with a critical lines and quantum phase transitions. By investigating the deformed MPS, we find various types of mixed states emergent from the ground states of the TFIM, and clarify phase transitions between them. In that study, strong and weak $Z_2$ symmetries play an important role, for which we introduce efficient order parameters, such as Rényi-2 correlators, entanglement entropy, etc., in the doubled Hilbert space.

11 pages, 7 figures; version to appear in Phys. Rev. B

References in corpus (17)

• Logical quantum processor based on reconfigurable atom arrays
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Topological Order and Conformal Quantum Critical Points
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Quantum criticality under decoherence or weak measurement
• Gauging quantum states: from global to local symmetries in many-body systems
• A quantum topological phase transition at the microscopic level
• Average Symmetry-Protected Topological Phases
• Intrinsic Mixed-state Topological Order
• Gapless Coulomb state emerging from a self-dual topological tensor-network state
• Symmetry protected topological phases under decoherence
• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Tensor Network Python (TeNPy) version 1
• MERA for Spin Chains with Continuously Varying Criticality
• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits
• System-environment entanglement phase transitions

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