Exactly solvable models in quantum many-body dynamics provide valuable insights into many interesting physical phenomena and serve as platforms for rigorously investigating fundamental theoretical questions. Nevertheless, they are extremely rare and existing solvable models and solution techniques have serious limitations. In this paper, we present a family of exactly solvable unitary circuits that model quantum many-body dynamics in discrete space and time. Unlike many previous solvable models, one can exactly compute the full quantum dynamics initialized from any matrix product state in this family of models. The time evolution of local observables and correlations, the linear growth of Rényi entanglement entropy, spatiotemporal correlations, and out-of-time-order correlations are all exactly computable. A key property of these models enabling the exact solution is that any time-evolved local operator is an exact matrix product operator with a finite bond dimension, even at arbitrarily long times, which we prove using the underlying C * -(weak) Hopf algebra structure along with tensor network techniques. We lay down the general framework for construction and solution of this family of models, and give several explicit examples. In particular, we study in detail a model constructed out of a C * -weak Hopf algebra that is very close to a Floquet version of the PXP model, and the exact results we obtain may shed light on the phenomenon of quantum many-body scars, and more generally, Floquet quantum dynamics in constrained systems.Exactly solvable models in quantum many-body dynamics provide valuable insights into many interesting physical phenomena and serve as platforms for rigorously investigating fundamental theoretical questions. Nevertheless, they are extremely rare and existing solvable models and solution techniques have serious limitations. In this paper, we present a family of exactly solvable unitary circuits that model quantum many-body dynamics in discrete space and time. Unlike many previous solvable models, one can exactly compute the full quantum dynamics initialized from any matrix product state in this family of models. The time evolution of local observables and correlations, the linear growth of Rényi entanglement entropy, spatiotemporal correlations, and out-of-time-order correlations are all exactly computable. A key property of these models enabling the exact solution is that any time-evolved local operator is an exact matrix product operator with a finite bond dimension, even at arbitrarily long times, which we prove using the underlying C * -(weak) Hopf algebra structure along with tensor network techniques. We lay down the general framework for construction and solution of this family of models, and give several explicit examples. In particular, we study in detail a model constructed out of a C * -weak Hopf algebra that is very close to a Floquet version of the PXP model, and the exact results we obtain may shed light on the phenomenon of quantum many-body scars, and more generally, Floquet quantum dynamics in constrained systems.

arXiv:2409.17215Physical review. B./Physical review. BMar 24, 20256 citations

Solvable Quantum Circuits from Spacetime Lattices

Michael A. Rampp, Suhail A. Rather, Pieter W. Claeys

In recent years dual-unitary circuits and their multi-unitary generalizations have emerged as exactly solvable yet chaotic models of quantum many-body dynamics. However, a systematic picture for the solvability of multi-unitary dynamics remains missing. We present a framework encompassing a large class of such non-integrable models with exactly solvable dynamics, which we term \emph{completely reducible} circuits. In these circuits, the entanglement membrane determining operator growth and entanglement dynamics can be characterized analytically. Completely reducible circuits extend the notion of space-time symmetry to more general lattice geometries, breaking dual-unitarity globally but not locally, and allow for a rich phenomenology going beyond dual-unitarity. As example, we introduce circuits that support four and five directions of information flow. We derive a general expression for the entanglement line tension in terms of the pattern of information flow in spacetime. The solvability is shown to be related to the absence of knots of this information flow, connecting entanglement dynamics to the Kauffman bracket as knot invariant. Building on these results, we propose that in general non-integrable dynamics the curvature of the entanglement line tension can be interpreted as a density of information transport. Our results provide a new and unified framework for exactly solvable models of many-body quantum chaos, encompassing and extending known constructions.In recent years dual-unitary circuits and their multi-unitary generalizations have emerged as exactly solvable yet chaotic models of quantum many-body dynamics. However, a systematic picture for the solvability of multi-unitary dynamics remains missing. We present a framework encompassing a large class of such non-integrable models with exactly solvable dynamics, which we term \emph{completely reducible} circuits. In these circuits, the entanglement membrane determining operator growth and entanglement dynamics can be characterized analytically. Completely reducible circuits extend the notion of space-time symmetry to more general lattice geometries, breaking dual-unitarity globally but not locally, and allow for a rich phenomenology going beyond dual-unitarity. As example, we introduce circuits that support four and five directions of information flow. We derive a general expression for the entanglement line tension in terms of the pattern of information flow in spacetime. The solvability is shown to be related to the absence of knots of this information flow, connecting entanglement dynamics to the Kauffman bracket as knot invariant. Building on these results, we propose that in general non-integrable dynamics the curvature of the entanglement line tension can be interpreted as a density of information transport. Our results provide a new and unified framework for exactly solvable models of many-body quantum chaos, encompassing and extending known constructions.

quant-pharXiv:2512.15871Dec 19, 20250 citations

Dynamics of quantum observables in entangled states

C. Sudheesh, S. Lakshmibala, V. Balakrishnan

Physics Letters AJun 9, 200912 citations

Realizing exactly solvable SU(N) magnets with thermal atoms

Michael E. Beverland, Gorjan Alagic, Michael J. Martin +3 more

We show that $n$ thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the ${S}_{n}$ symmetry that permutes atoms occupying different vibrational levels of the trap and the $\mathrm{SU}(N)$ symmetry associated with $N$ nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this $\mathrm{SU}(N$ ) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.We show that $n$ thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the ${S}_{n}$ symmetry that permutes atoms occupying different vibrational levels of the trap and the $\mathrm{SU}(N)$ symmetry associated with $N$ nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this $\mathrm{SU}(N$) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.

arXiv:1409.3234Physical Review AMay 6, 201623 citations

Quantum Dynamics of Bound Entangled States

Zhu, Guoqiang, Wang +1 more

理论物理通讯：英文版Jan 1, 20080 citations

We show that

n

thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the

{S}_{n}

symmetry that permutes atoms occupying different vibrational levels of the trap and the

\mathrm{SU}(N)

symmetry associated with

N

nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this

\mathrm{SU}(N

) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.