Publications

Order by: publication date number of citations

• Continuous Néel-VBS quantum phase transition in non-local one-dimensional systems with SO(3) symmetry

  Chao-Ming Jian, Yichen Xu, Xiao-Chuan Wu, Cenke Xu

  SciPost Phys. 10, 033 (2021) · published 12 February 2021 | Toggle abstract · pdf

  One dimensional $(1d)$ interacting systems with local Hamiltonians can be studied with various well-developed analytical methods. Recently novel $1d$ physics was found numerically in systems with either spatially nonlocal interactions, or at the $1d$ boundary of $2d$ quantum critical points, and the critical fluctuation in the bulk also yields effective nonlocal interactions at the boundary. This work studies the edge states at the $1d$ boundary of $2d$ strongly interacting symmetry protected topological (SPT) states, when the bulk is driven to a disorder-order phase transition. We will take the $2d$ Affleck-Kennedy-Lieb-Tasaki (AKLT) state as an example, which is a SPT state protected by the $SO(3)$ spin symmetry and spatial translation. We found that the original $(1+1)d$ boundary conformal field theory of the AKLT state is unstable due to coupling to the boundary avatar of the bulk quantum critical fluctuations. When the bulk is fixed at the quantum critical point, within the accuracy of our expansion method, we find that by tuning one parameter at the boundary, there is a generic direct transition between the long range antiferromagnetic N\'{e}el order and the valence bond solid (VBS) order. This transition is very similar to the Néel-VBS transition recently found in numerical simulation of a spin-1/2 chain with nonlocal spatial interactions. Connections between our analytical studies and recent numerical results concerning the edge states of the $2d$ AKLT-like state at a bulk quantum phase transition will also be discussed.

  27 citations

• Unifying constructions of non-invertible symmetries

  Lakshya Bhardwaj, Sakura Schäfer-Nameki, Apoorv Tiwari

  SciPost Phys. 15, 122 (2023) · published 28 September 2023 | Toggle abstract · pdf

  In the past year several constructions of non-invertible symmetries in Quantum Field Theory in $d≥3$ have appeared. In this paper we provide a unified perspective on these constructions. Central to this framework are so-called theta defects, which generalize the notion of theta-angles, and allow the construction of universal and non-universal topological symmetry defects. We complement this physical analysis by proposing a mathematical framework (based on higher-fusion categories) that converts the physical construction of non-invertible symmetries into a concrete computational scheme.

  27 citations

• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54

  Katja Klobas, Bruno Bertini

  SciPost Phys. 11, 106 (2021) · published 20 December 2021 | Toggle abstract · pdf

  We study the out-of-equilibrium dynamics of the quantum cellular automaton Rule 54 using a time-channel approach. We exhibit a family of (non-equilibrium) product states for which we are able to describe exactly the full relaxation dynamics. We use this to prove that finite subsystems relax to a one-parameter family of Gibbs states. We also consider inhomogeneous quenches. Specifically, we show that when the two halves of the system are prepared in two different solvable states, finite subsystems at finite distance from the centre eventually relax to the non-equilibrium steady state (NESS) predicted by generalised hydrodynamics. To the best of our knowledge, this is the first exact description of the relaxation to a NESS in an interacting system and, therefore, the first independent confirmation of generalised hydrodynamics for an inhomogeneous quench.

  27 citations

• A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice

  Ido Niesen, Philippe Corboz

  SciPost Phys. 3, 030 (2017) · published 28 October 2017 | Toggle abstract · pdf

  Using infinite projected entangled pair states, we study the ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice directly in the thermodynamic limit. We find an unexpected partially nematic partially magnetic phase in between the antiferroquadrupolar and ferromagnetic regions. Furthermore, we describe all observed phases and discuss the nature of the phase transitions involved.

  27 citations

• Living on the walls of super-QCD

  Vladimir Bashmakov, Francesco Benini, Sergio Benvenuti, Matteo Bertolini

  SciPost Phys. 6, 044 (2019) · published 15 April 2019 | Toggle abstract · pdf

  We study BPS domain walls in four-dimensional $\mathcal{N}=1$ massive SQCD with gauge group $SU(N)$ and $F<N$ flavors. We propose a class of three-dimensional Chern-Simons-matter theories to describe the effective dynamics on the walls. Our proposal passes several checks, including the exact matching between its vacua and the solutions to the four-dimensional BPS domain wall equations, that we solve in the small mass regime. As the flavor mass is varied, domain walls undergo a second-order phase transition, where multiple vacua coalesce into a single one. For special values of the parameters, the phase transition exhibits supersymmetry enhancement. Our proposal includes and extends previous results in the literature, providing a complete picture of BPS domain walls for $F<N$ massive SQCD. A similar picture holds also for SQCD with gauge group $Sp(N)$ and $F < N+1$ flavors.

  26 citations

• Equilibrium fluctuations in maximally noisy extended quantum systems

  Michel Bauer, Denis Bernard, Tony Jin

  SciPost Phys. 6, 045 (2019) · published 16 April 2019 | Toggle abstract · pdf

  We introduce and study a class of models of free fermions hopping between neighbouring sites with random Brownian amplitudes. These simple models describe stochastic, diffusive, quantum, unitary dynamics. We focus on periodic boundary conditions and derive the complete stationary distribution of the system. It is proven that the generating function of the latter is provided by the Harish-Chandra-Itzykson-Zuber integral which allows us to access all fluctuations of the system state. The steady state is characterized by non trivial correlations which have a topological nature. Diagrammatic tools appropriate for the study of these correlations are presented. In the thermodynamic large system size limit, the system approaches a non random equilibrium state plus occupancy and coherence fluctuations of magnitude scaling proportionally with the inverse of the square root of the volume. The large deviation function for those fluctuations is determined. Although decoherence is effective on the mean steady state, we observe that sub-leading fluctuating coherences are dynamically produced from the inhomogeneities of the initial occupancy profile.

  26 citations

• Bulk Renormalization Group Flows and Boundary States in Conformal Field Theories

  John Cardy

  SciPost Phys. 3, 011 (2017) · published 12 August 2017 | Toggle abstract · pdf

  We propose using smeared boundary states $e^{-\tau H}|\cal B\rangle$ as variational approximations to the ground state of a conformal field theory deformed by relevant bulk operators. This is motivated by recent studies of quantum quenches in CFTs and of the entanglement spectrum in massive theories. It gives a simple criterion for choosing which boundary state should correspond to which combination of bulk operators, and leads to a rudimentary phase diagram of the theory in the vicinity of the RG fixed point corresponding to the CFT, as well as rigorous upper bounds on the universal amplitude of the free energy. In the case of the 2d minimal models explicit formulae are available. As a side result we show that the matrix elements of bulk operators between smeared Ishibashi states are simply given by the fusion rules of the CFT.

  26 citations

• Investigating ultrafast quantum magnetism with machine learning

  Giammarco Fabiani, Johan H. Mentink

  SciPost Phys. 7, 004 (2019) · published 5 July 2019 | Toggle abstract · pdf

  We investigate the efficiency of the recently proposed Restricted Boltzmann Machine (RBM) representation of quantum many-body states to study both the static properties and quantum spin dynamics in the two-dimensional Heisenberg model on a square lattice. For static properties we find close agreement with numerically exact Quantum Monte Carlo results in the thermodynamical limit. For dynamics and small systems, we find excellent agreement with exact diagonalization, while for systems up to N=256 spins close consistency with interacting spin-wave theory is obtained. In all cases the accuracy converges fast with the number of network parameters, giving access to much bigger systems than feasible before. This suggests great potential to investigate the quantum many-body dynamics of large scale spin systems relevant for the description of magnetic materials strongly out of equilibrium.

  26 citations

• Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions

  Etienne Granet, Maurizio Fagotti, Fabian H. L. Essler

  SciPost Phys. 9, 033 (2020) · published 4 September 2020 | Toggle abstract · pdf

  We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.

  26 citations

• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model

  Etienne Granet, Fabian H. L. Essler

  SciPost Phys. 9, 082 (2020) · published 7 December 2020 | Toggle abstract · pdf

  We introduce a framework for calculating dynamical correlations in the Lieb-Liniger model in arbitrary energy eigenstates and for all space and time, that combines a Lehmann representation with a $1/c$ expansion. The $n^{\rm th}$ term of the expansion is of order $1/c^n$ and takes into account all $\lfloor \tfrac{n}{2}\rfloor+1$ particle-hole excitations over the averaging eigenstate. Importantly, in contrast to a ``bare" $1/c$ expansion it is uniform in space and time. The framework is based on a method for taking the thermodynamic limit of sums of form factors that exhibit non integrable singularities. We expect our framework to be applicable to any local operator.\\ We determine the first three terms of this expansion and obtain an explicit expression for the density-density dynamical correlations and the dynamical structure factor at order $1/c^2$. We apply these to finite-temperature equilibrium states and non-equilibrium steady states after quantum quenches. We recover predictions of (nonlinear) Luttinger liquid theory and generalized hydrodynamics in the appropriate limits, and are able to compute sub-leading corrections to these.

  26 citations