Floquet dynamical chiral spin liquid at finite frequency

Abstract

Chiral Spin Liquids (CSL) are quantum spin analogs of electronic Fractional Chern Insulators. Their realizations on ultracold-atom or Rydberg-atom platforms remain very challenging. Recently, a setup of time-periodic modulations of nearest-neighbor Heisenberg couplings applied on an initial genuine spin liquid state on the square lattice has been proposed to stabilize a (Abelian) ${\mathbb{Z}}_2$ CSL phase. In the high-frequency limit, it was shown that time evolution can be described in terms of a static effective chiral Hamiltonian. Here we revisit this proposal and consider drives at lower frequency in a regime where the high-frequency Magnus expansion fails. We show that a Dynamical CSL (DCSL) is nevertheless stabilized in a finite range of frequency. The topological nature of this dynamical phase, as well as its instability below a critical frequency, is connected to specific features of the Floquet pseudo-energy spectrum. We also show that the DCSL can be represented faithfully by a two-dimensional time-periodic tensor network and, as in the static case, topological order is associated to a tensor gauge symmetry (${\mathbb{Z}}_2$ in that case).

11 pages, 6 figures, 2 tables

References in corpus (14)

• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• An exact chiral spin liquid with non-Abelian anyons
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Realization of a fractional quantum Hall state with ultracold atoms
• Chiral topological spin liquids with projected entangled pair states
• Non-Abelian Floquet Spin Liquids in a Digital Rydberg Simulator
• Engineering and probing non-Abelian chiral spin liquids using periodically driven ultracold atoms
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Topology and localization of a periodically driven Kitaev model
• High-frequency expansions for time-periodic Lindblad generators
• Chiral spin liquids on the kagome lattice with projected entangled simplex states
• Quantum state preparation of topological chiral spin liquids via Floquet engineering

Cited by in corpus (2)

• The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation
• Detuning the Floquet anomalous chiral spin liquid