Publications

Order by: publication date number of citations

• Rényi entropies and negative central charges in non-Hermitian quantum systems

  Yi-Ting Tu, Yu-Chin Tzeng, Po-Yao Chang

  SciPost Phys. 12, 194 (2022) · published 13 June 2022 | Toggle abstract · pdf

  Quantum entanglement is one essential element to characterize many-body quantum systems. However, the entanglement measures are mostly discussed in Hermitian systems. Here, we propose a natural extension of entanglement and R\'enyi entropies to non-Hermitian quantum systems. There have been other proposals for the computation of these quantities, which are distinct from what is proposed in the current paper. We demonstrate the proposed entanglement quantities which are referred to as generic entanglement and R\'enyi entropies. These quantities capture the desired entanglement properties in non-Hermitian critical systems, where the low-energy properties are governed by the non-unitary conformal field theories (CFTs). We find excellent agreement between the numerical extrapolation of the negative central charges from the generic entanglement/R\'enyi entropy and the non-unitary CFT prediction. Furthermore, we apply the generic entanglement/R\'enyi entropy to symmetry-protected topological phases with non-Hermitian perturbations. We find the generic $n$-th R\'enyi entropy captures the expected entanglement property, whereas the traditional R\'enyi entropy can exhibit unnatural singularities due to its improper definition.

  34 citations

• Statistics of correlation functions in the random Heisenberg chain

  Luis Colmenarez, Paul A. McClarty, Masudul Haque, David J. Luitz

  SciPost Phys. 7, 064 (2019) · published 21 November 2019 | Toggle abstract · pdf

  Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) -- at least in one dimensional systems -- leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators. For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of eigenstate correlation functions across the entire phase diagram. We find gaussian distributions at weak disorder, as predicted by pure ETH. At intermediate disorder -- in the thermal phase -- we find further evidence for anomalous thermalization in the form of heavy tails of the distributions. In the MBL phase, we observe peculiar features of the correlator distributions: a strong asymmetry in $S_i^z S_{i+r}^z$ correlators skewed towards negative values; and a multimodal distribution for spin-flip correlators. A quantitative quasi-degenerate perturbation theory calculation of these correlators yields a surprising agreement of the full distribution with the exact results, revealing, in particular, the origin of the multiple peaks in the spin-flip correlator distribution as arising from the resonant and off-resonant admixture of spin configurations. The distribution of the $S_i^zS_{i+r}^z$ correlator exhibits striking differences between the MBL and Anderson insulator cases.

  33 citations

• Information dynamics in a model with Hilbert space fragmentation

  Dominik Hahn, Paul A. McClarty, David J. Luitz

  SciPost Phys. 11, 074 (2021) · published 6 October 2021 | Toggle abstract · pdf

  The fully frustrated ladder - a quasi-1D geometrically frustrated spin one half Heisenberg model - is non-integrable with local conserved quantities on rungs of the ladder, inducing the fragmentation of the Hilbert space into sectors composed of singlets and triplets on rungs. We explore the far-from-equilibrium dynamics of this model through the entanglement entropy and out-of-time-ordered correlators (OTOC). The post-quench dynamics of the entanglement entropy is highly anomalous as it shows clear non-damped revivals that emerge from short connected chunks of triplets and whose persistence is therefore a consequence of fragmentation. We find that the maximum value of the entropy follows from a picture where coherences between different fragments co-exist with perfect thermalization within each fragment. This means that the eigenstate thermalization hypothesis holds within all sufficiently large Hilbert space fragments. The OTOC shows short distance oscillations arising from short coupled fragments, which become decoherent at longer distances, and a sub-ballistic spreading and long distance exponential decay stemming from an emergent length scale tied to fragmentation.

  33 citations

• Correlations and commuting transfer matrices in integrable unitary circuits

  Pieter W. Claeys, Jonah Herzog-Arbeitman, Austen Lamacraft

  SciPost Phys. 12, 007 (2022) · published 6 January 2022 | Toggle abstract · pdf

  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.

  33 citations

• Aspects of categorical symmetries from branes: SymTFTs and generalized charges

  Fabio Apruzzi, Federico Bonetti, Dewi S.W. Gould, Sakura Schäfer-Nameki

  SciPost Phys. 17, 025 (2024) · published 29 July 2024 | Toggle abstract · pdf

  Recently it has been observed that branes in geometric engineering and holography have a striking connection with generalized global symmetries. In this paper we argue that branes, in a certain topological limit, not only furnish the symmetry generators, but also encode the so-called Symmetry Topological Field Theory (or SymTFT). For a $d$-dimensional QFT, this is a $(d+1)$-dimensional topological field theory, whose topological defects encode both the symmetry generators (invertible or non-invertible) and the generalized charges. Mathematically, the topological defects form the Drinfeld center of the symmetry category of the QFT. In this paper we derive the SymTFT and the Drinfeld center topological defects directly from branes. Central to the identification of these are Hanany-Witten brane configurations, which encode both topological couplings in the SymTFT and the generalized charges under the symmetries. We exemplify the general analysis with examples of QFTs realized in geometric engineering or holography.

  33 citations

• Reports of my demise are greatly exaggerated: $N$-subjettiness taggers take on jet images

  Liam Moore, Karl Nordström, Sreedevi Varma, Malcolm Fairbairn

  SciPost Phys. 7, 036 (2019) · published 24 September 2019 | Toggle abstract · pdf

  We compare the performance of a convolutional neural network (CNN) trained on jet images with dense neural networks (DNNs) trained on n-subjettiness variables to study the distinguishing power of these two separate techniques applied to top quark decays. We find that they perform almost identically and are highly correlated once jet mass information is included, which suggests they are accessing the same underlying information which can be intuitively understood as being contained in 4-, 5-, 6-, and 8-body kinematic phase spaces depending on the sample. This suggests both of these methods are highly useful for heavy object tagging and provides a tentative answer to the question of what the image network is actually learning.

  33 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.

  33 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.

  33 citations

• Thermal conformal blocks

  Yan Gobeil, Alexander Maloney, Gim Seng Ng, Jie-qiang Wu

  SciPost Phys. 7, 015 (2019) · published 1 August 2019 | Toggle abstract · pdf

  We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second order Casimir differential equations and have integral representations related to AdS Witten diagrams. We give an analytic formula for the scalar conformal block in terms of generalized hypergeometric functions. As an application, we deduce an asymptotic formula for the three-point coeffcients of primary operators in the limit where two of the operators are heavy.

  33 citations

• Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

  Grégoire Misguich, Nicolas Pavloff, Vincent Pasquier

  SciPost Phys. 7, 025 (2019) · published 29 August 2019 | Toggle abstract · pdf

  We study the dynamics of a spin-1/2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (x, y and z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schr\"odinger equation is used to construct a variational solution capturing several aspects of the problem.

  33 citations