Integrable Quantum Circuits from the Star-Triangle Relation

Abstract

The star-triangle relation plays an important role in the realm of exactly solvable models, offering exact results for classical two-dimensional statistical mechanical models. In this article, we construct integrable quantum circuits using the star-triangle relation. Our construction relies on families of mutually commuting two-parameter transfer matrices for statistical mechanical models solved by the star-triangle relation, and differs from previously known constructions based on Yang-Baxter integrable vertex models. At special value of the spectral parameter, the transfer matrices are mapped into integrable quantum circuits, for which infinite families of local conserved charges can be derived. We demonstrate the construction by giving two examples of circuits acting on a chain of $Q-$state qudits: $Q$-state Potts circuits, whose integrability has been conjectured recently by Lotkov et al., and ${\mathbb{Z}}_Q$ circuits, which are novel to our knowledge. In the first example, we present for $Q=3$ a connection to the Zamolodchikov-Fateev 19-vertex model.

arXiv comment25 pages, 9 figures. Accepted by Quantum

References in corpus (47)

• Thermalization and its mechanism for generic isolated quantum systems
• Quantum Simulation
• Floquet Time Crystals
• On the phase structure of driven quantum systems
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Generalized Gibbs ensemble in integrable lattice models
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Universal digital quantum simulation with trapped ions
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Time evolution of local observables after quenching to an integrable model
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Floquet topological insulators
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• Solution of a minimal model for many-body quantum chaos
• Topological phases with parafermions: theory and blueprints
• Exact dynamics in dual-unitary quantum circuits
• The Quench Action
• What is an integrable quench?
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Generating Many Majorana Modes via Periodic Driving: A Superconductor Model
• Integrable Trotterization: Local Conservation Laws and Boundary Driving
• Free parafermions
• Numerical study of the chiral ${\mathbb{Z}}_3$ quantum phase transition in one spatial dimension
• Hirota equation as an example of integrable symplectic map
• Integrable Floquet dynamics
• Dissipative quantum Ising chain as a non-Hermitian Ashkin-Teller model
• Floquet control of quantum dissipation in spin chains
• Phase diagram of the S=1/2 quantum spin chain with bond alternation
• Lattice regularization of massive and massless integrable field theories
• Quasi-local conserved charges and spin transport in spin-$1$ integrable chains
• Integrable nonunitary open quantum circuits
• Control of tunneling in an atomtronic switching device
• Onsager symmetries in $U(1)$-invariant clock models
• Atomtronic protocol designs for NOON states
• Algebraic Bethe Circuits
• The "not-A", RSPT and Potts phases in an $S_3$-invariant chain
• Conserved charges in the quantum simulation of integrable spin chains
• Complexity and Floquet dynamics: non-equilibrium Ising phase transitions
• Floquet integrability and long-range entanglement generation in the one-dimensional quantum Potts model
• Generalised Onsager Algebra in Quantum Lattice Models
• Conjectures on Hidden Onsager Algebra Symmetries in Interacting Quantum Lattice Models
• An Ising-type formulation of the six-vertex model
• Fateev-Zamolodchikov and Kashiwara-Miwa models: boundary star-triangle relations and surface critical properties
• Quantum quench in a driven Ising chain
• Integrable Floquet systems related to logarithmic conformal field theory

Cited by in corpus (11)

• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Strong zero modes in integrable quantum circuits
• Operator dynamics and entanglement in space-time dual Hadamard lattices
• Exactly solvable many-body dynamics from space-time duality
• Quantum Zeno Effect in Noisy Integrable Quantum Circuits for Impurity Models
• Quantum many-body spin ratchets
• Integrability is generic in homogeneous U(1)-invariant nearest-neighbor qubit circuits
• Integrability of Goldilocks quantum cellular automata
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Majorana fermions solve the tetrahedron equations as well as higher simplex equations
• On correlation functions in models related to the Temperley-Lieb algebra