# Pieter W. Claeys

pwclaeys@gmail.com# News

## CMT Forum at Oxford University

17 January 2022Next Wednesday, January 26th, I will be presenting some new results (in person!) on **dual-unitary circuits** at the **Condensed Matter Theory Forum** at the Rudolf Peierls Centre for Theoretical Physics at Oxford University.

More information can be found here.

**Title**: Dual-unitary circuit dynamics

**Abstract**: Quantum lattice models with time evolution governed by local unitary quantum circuits can serve as a minimal model for the study of general unitary dynamics governed by local interactions. Although such circuit dynamics exhibit many of the features expected of generic many-body dynamics, exact results generally require the presence of randomness in the circuit. I will discuss dual-unitary circuits characterized by an underlying space-time symmetry, and show how they give rise to exactly solvable models for ergodic and non-ergodic thermalization for correlations and the scrambling of out-of-time-order correlators. Combining dual-unitary dynamics with projective measurements, I will also make the connection with random matrix theory and show how measurements can give rise to uniformly distributed states and a quantum state-design.

## New publications

17 January 2022Two of our recent papers have now been published, both in fully open access journals! Our work on **Correlations and commuting transfer matrices in integrable unitary circuits** is now published here in SciPost Physics, and **Dissipative dynamics in open XXZ Richardson-Gaudin models** appeared in the latest issue of Physical Review Research. As usual, the SciPost referee reports can be found along with the submission. Abstracts below.

**Correlations and commuting transfer matrices in integrable unitary circuits**: *We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer Hermitian and differ from the ones guaranteeing local conservation laws, but remain mutually commuting at different values of the spectral parameter defining the circuit. Exact eigenstates can still be constructed as a Bethe ansatz, but while these transfer matrices are diagonalizable in the inhomogeneous case, the homogeneous limit corresponds to an exceptional point where multiple eigenstates coalesce and Jordan blocks appear. Remarkably, the complete set of (generalized) eigenstates is only obtained when taking into account a combinatorial number of nontrivial vacuum states. In all cases, the Bethe equations reduce to those of the integrable spin-1 chain and exhibit a global SU(2) symmetry, significantly reducing the total number of eigenstates required in the calculation of correlation functions. A similar construction is shown to hold for the calculation of out-of-time-order correlations.*

**Dissipative dynamics in open XXZ Richardson-Gaudin models**: *In specific open systems with collective dissipation the Liouvillian can be mapped to a non-Hermitian Hamiltonian. We here consider such a system where the Liouvillian is mapped to an XXZ Richardson-Gaudin integrable model and detail its exact Bethe ansatz solution. While no longer Hermitian, the Hamiltonian is pseudo-Hermitian/PT-symmetric, and as the strength of the coupling to the environment is increased the spectrum in a fixed symmetry sector changes from a broken pseudo-Hermitian phase with complex conjugate eigenvalues to a pseudo-Hermitian phase with real eigenvalues, passing through a series of exceptional points and associated dissipative quantum phase transitions. The homogeneous limit supports a nontrivial steady state, and away from this limit this state gives rise to a slow logarithmic growth of the decay rate (spectral gap) with system size. Using the exact solution, it is furthermore shown how at large coupling strengths the ratio of the imaginary to the real part of the eigenvalues becomes approximately quantized in the remaining symmetry sectors.*

## Talks and workshops

08 November 2021Some news on various talks:

This Wednesday and Thursday I will be presenting at and participating in the virtual workshop on

**Spacetime Duality in Quantum Circuits**organized by Suhail Ahmad Rather, Aravinda S. and Arul Lakshminarayan.As written on the website: The general notions of duality and symmetry act as powerful tools in understanding many-body classical or quantum systems. A particular type of duality, dubbed spacetime duality, due to the interchange of the roles of space and time, has been recently applied to locally interacting quantum lattice models and offers remarkable advantages and insights. These include building solvable models of many-body quantum chaos, toy models of many-body non-unitary dynamics, dynamical phase transitions and quantum computation. The roots of the duality lie in quantum information theory and the notions of operator entanglement, entangling power, multipartite entangled states, and quantum designs play a central role. This focus workshop will bring together some of the pioneers in the area and will highlight recent progress and future directions in such spacetime dual models. It is an activity of the Center for Quantum Information Theory of Matter and Spacetime, IIT Madras, and the Department of Physics, IIT Tirupati.

My talk on our recent work on the

**Absence of superdiffusion in certain random spin models**at the Leeds-Loughborough-Nottingham seminar series is now available on YouTube.Last but not least, this Friday I will be presenting some of our work on

**dual-unitary circuits**at the mini-workshop organized to celebrate the 50th birthday of Jean-Sébastien Caux!