Many Body Quantum Chaos and Dual Unitarity Round-a-Face

Abstract

We propose a new type of locally interacting quantum circuits which are generated by unitary interactions round-a-face (IRF). Specifically, we discuss a set (or manifold) of dual-unitary IRFs with local Hilbert space dimension $d$ (DUIRF$(d)$) which generate unitary evolutions both in space and time directions of an extended 1+1 dimensional lattice. We show how arbitrary dynamical correlation functions of local observables can be evaluated in terms of finite dimensional completely positive trace preserving unital maps, in complete analogy to recently studied circuits made of dual unitary brick gates (DUBG). In fact, we show that the simplest non-trivial (non-vanishing) local correlation functions in dual-unitary IRF circuits involve observables non-trivially supported on at least two sites. We completely characterise the 10-dimensional manifold of DUIRF$(2)$ for qubits ($d=2$) and provide, for $d=3,4,5,6,7$, empirical estimates of its dimensionality based on numerically determined dimensions of tangent spaces at an ensemble of random instances of dual-unitary IRF gates. In parallel, we apply the same algorithm to determine $\dim \mathrm{DUBG}(d)$ and show that they are of similar order though systematically larger than $\dim \mathrm{DUIRF}(d)$ for $d=2,3,4,5,6,7$. It is remarkable that both sets have rather complex topology for $d\ge 3$ in the sense that the dimension of the tangent space varies among different randomly generated points of the set. Finally, we provide additional data on dimensionality of the chiral extension of DUBG circuits with distinct local Hilbert spaces of dimensions $d\ne d^{\prime }$ residing at even/odd lattice sites.

11 pages in RevTeX, 10 figures, submitted to Chaos, focus issue "Dissipative Quantum Chaos"

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• Construction and local equivalence of dual-unitary operators: from dynamical maps to quantum combinatorial designs
• Hierarchical generalization of dual unitarity
• Dual unitary circuits in random geometries
• Circuits of space and time quantum channels
• Ternary unitary quantum lattice models and circuits in $2+1$ dimensions
• Quantum information spreading in generalised dual-unitary circuits
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• Operator dynamics and entanglement in space-time dual Hadamard lattices
• Exactly solvable many-body dynamics from space-time duality
• Exact Hidden Markovian Dynamics in Quantum Circuits
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
• Fundamental charges for dual-unitary circuits
• Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points
• Entanglement of Disjoint Intervals in Dual-Unitary Circuits: Exact Results
• Integrability of Goldilocks quantum cellular automata
• Entanglement in dual unitary quantum circuits with impurities
• Solvable Quantum Circuits in Tree+1 Dimensions
• Geometric constructions of generalized dual-unitary circuits from biunitarity
• Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps