Fisher zeros and persistent temporal oscillations in non-unitary quantum circuits

Abstract

We present a quantum circuit with measurements and post-selection that exhibits a panoply of space- and/or time-ordered phases, from ferromagnetic order to spin-density waves to time crystals. Unlike the time crystals that have been found in unitary models, those that occur here are \emph{incommensurate} with the drive frequency. The period of the incommensurate time-crystal phase may be tuned by adjusting the circuit parameters. We demonstrate that the phases of our quantum circuit, including the inherently non-equilibrium dynamical ones, correspond to complex-temperature equilibrium phases of the exactly solvable square-lattice anisotropic Ising model.

v1-->v2: significantly revised, new co-author added; small typo fixed in the most recent version 3

References in corpus (8)

• Tensor renormalization group approach to 2D classical lattice models
• Absence of Quantum Time Crystals
• Critical properties of the measurement-induced transition in random quantum circuits
• Minimally Entangled Typical Thermal State Algorithms
• Postselection-free entanglement dynamics via spacetime duality
• A Brief History of Time Crystals
• Spacetime duality between localization transitions and measurement-induced transitions
• Limit cycle phase in driven-dissipative spin systems

Cited by in corpus (6)

• Crystalline Quantum Circuits
• Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
• Exact Fisher zeros and thermofield dynamics across a quantum critical point
• Signatures of quantum criticality in the complex inverse temperature plane
• Robust Oscillations and Edge Modes in Nonunitary Floquet Systems
• Unpolarized prethermal discrete time crystal