Publications

Order by: publication date number of citations

• Functional flows for complex effective actions

  Friederike Ihssen, Jan M. Pawlowski

  SciPost Phys. 15, 074 (2023) · published 31 August 2023 | Toggle abstract · pdf

  In the present work we set up a general functional renormalisation group framework for the computation of complex effective actions. For explicit computations we consider both flows of the Wilsonian effective action and the one-particle irreducible (1PI) effective action. The latter is based on an appropriate definition of a Legendre transform for complex actions, and we show its validity by comparison to exact results in zero dimensions, as well as a comparison to results for the Wilsonian effective action. In the present implementations of the general approaches, the flow of the Wilsonian effective action has a wider range of applicability and we obtain results for the effective potential of complex fields in $\phi^4$-theories from zero up to four dimensions. These results are also compared with results from the 1PI effective action within its range of applicability. The complex effective action also allows us to determine the location of the Lee-Yang zeros for general parameter values. We also discuss the extension of the present results to general theories including QCD.

  5 citations

• Quasi-localized vibrational modes, boson peak and sound attenuation in model mass-spring networks

  Shivam Mahajan, Massimo Pica Ciamarra

  SciPost Phys. 15, 069 (2023) · published 23 August 2023 | Toggle abstract · pdf

  We introduce an algorithm that constructs disordered mass-spring networks whose elastic properties mimic that of glasses by tuning the fluctuations of the local elastic properties, keeping fixed connectivity and controlling the prestress. In two dimensions, the algorithm reproduces the dependence of glasses' vibrational properties, such as quasi-localised vibrational modes and Boson peak, on the degree of stability. The sound attenuation displays Rayleigh scattering and disorder-broadening regimes at different frequencies, and the attenuation rate decreases with increased stability. Our results establish a strong connection between the vibrational features of disordered solids and the fluctuations of the local elastic properties and provide a new approach to investigating glasses' vibrational anomalies.

  4 citations

• Diagnosing weakly first-order phase transitions by coupling to order parameters

  Jonathan D'Emidio, Alexander A. Eberharter, Andreas M. Läuchli

  SciPost Phys. 15, 061 (2023) · published 14 August 2023 | Toggle abstract · pdf

  The hunt for exotic quantum phase transitions described by emergent fractionalized degrees of freedom coupled to gauge fields requires a precise determination of the fixed point structure from the field theoretical side, and an extreme sensitivity to weak first-order transitions from the numerical side. Addressing the latter, we revive the classic definition of the order parameter in the limit of a vanishing external field at the transition. We demonstrate that this widely understood, yet so far unused approach provides a diagnostic test for first-order versus continuous behavior that is distinctly more sensitive than current methods. We first apply it to the family of $Q$-state Potts models, where the nature of the transition is continuous for $Q\leq4$ and turns (weakly) first order for $Q>4$, using an infinite system matrix product state implementation. We then employ this new approach to address the unsettled question of deconfined quantum criticality in the $S=1/2$ Néel to valence bond solid transition in two dimensions, focusing on the square lattice $J$-$Q$ model. Our quantum Monte Carlo simulations reveal that both order parameters remain finite at the transition, directly confirming a first-order scenario with wide reaching implications in condensed matter and quantum field theory.

  13 citations

• Traveling discontinuity at the quantum butterfly front

  Camille Aron, Éric Brunet, Aditi Mitra

  SciPost Phys. 15, 042 (2023) · published 2 August 2023 | Toggle abstract · pdf

  We formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential equations that effectively govern the dynamics of information spreading in generic dimensions. Their solutions show that scrambling propagates at the maximal speed set by the Fermi velocity. At early times, we find exponential growth at a rate set by the inelastic scattering. At late times, we find that scrambling is governed by shock-wave dynamics with traveling waves exhibiting a discontinuity at the boundary of the light cone. Notably, we find perfectly causal dynamics where the solutions do not spill outside of the light cone.

  2 citations

• Super-diffusion and crossover from diffusive to anomalous transport in a one-dimensional system

  Anupam Kundu

  SciPost Phys. 15, 038 (2023) · published 31 July 2023 | Toggle abstract · pdf

  We study transport in a one-dimensional lattice system with two conserved quantities - "volume" and energy. Considering a slowly evolving local equilibrium state that is slightly deviated from an underlying global equilibrium, we estimate the correction to the local equilibrium distribution. This correction arises mainly through the space-time correlations of some local currents. In the continuum limit, we show that the local equilibrium distribution along with the correction yields drift-diffusion equation for the "volume" and super-diffusion equation for the energy in the linear response regime as macroscopic hydrodynamics as one would obtain from non-linear fluctuating hydrodynamic theory. We find explicit expression of the super-diffusion equation. Further, we find diffusive correction to the super-diffusive evolution. Such a correction allows us to study a crossover from diffusive to anomalous transport. We demonstrate this crossover numerically through the spreading of an initially localized heat pulse in equilibrium as well as through the system size scaling of the stationary current in non-equilibrium steady state.

  1 citation

• Integrability and quench dynamics in the spin-1 central spin XX model

  Long-Hin Tang, David M. Long, Anatoli Polkovnikov, Anushya Chandran, Pieter W. Claeys

  SciPost Phys. 15, 030 (2023) · published 26 July 2023 | Toggle abstract · pdf

  Central spin models provide an idealized description of interactions between a central degree of freedom and a mesoscopic environment of surrounding spins. We show that the family of models with a spin-1 at the center and XX interactions of arbitrary strength with surrounding spins is integrable. Specifically, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. As in the homogenous limit, the states divide into two exponentially large classes: bright states, in which the spin-1 is entangled with its surroundings, and dark states, in which it is not. On resonance, the bright states further break up into two classes depending on their weight on states with central spin polarization zero. These classes are probed in quench dynamics wherein they prevent the central spin from reaching thermal equilibrium. In the single spin-flip sector we explicitly construct the bright states and show that the central spin exhibits oscillatory dynamics as a consequence of the semilocalization of these eigenstates. We relate the integrability to the closely related class of integrable Richardson-Gaudin models, and conjecture that the spin-$s$ central spin XX model is integrable for any $s$.

  6 citations

• Connected correlations in partitioning protocols: A case study and beyond

  Saverio Bocini

  SciPost Phys. 15, 027 (2023) · published 25 July 2023 | Toggle abstract · pdf

  The assumption of local relaxation in inhomogeneous quantum quenches allows to compute asymptotically the expectation value of local observables via hydrodynamic arguments known as generalized hydrodynamics (GHD). In this work we address formally the question of when an observable is local enough to be described by GHD using the playground of partitioning protocols and non-interacting time evolution. We show that any state evolving under a quadratic Hamiltonian can be described via a set of decoupled dynamical fields such that one of those fields can be identified with a space-time-dependent generalisation of the root density. By studying the contribution to a connected spin correlation of each of those fields independently, we derive the locality conditions under which an observable can be described using the root density only. That shows both the regime of validity for hydrodynamic approaches that aim at describing the asymptotic value of observables in term of the root density only, such as GHD, and the locality conditions necessary for Gaussianification to occur.

  3 citations

• Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach

  Philipp Strasberg

  SciPost Phys. 15, 024 (2023) · published 24 July 2023 | Toggle abstract · pdf

  Answers to the question how a classical world emerges from underlying quantum physics are revisited, connected and extended as follows. First, three distinct concepts are compared: decoherence in open quantum systems, consistent/decoherent histories and Kolmogorov consistency. Second, the crucial role of quantum Markovianity (defined rigorously) to connect these concepts is established. Third, using a random matrix theory model, quantum effects are shown to be exponentially suppressed in the measurement statistics of slow and coarse observables despite the presence of large amount of coherences. This is also numerically exemplified, and it highlights the potential and importance of non-integrability and chaos for the emergence of classicality.

  9 citations

• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum

  Caterina Zerba, Alessandro Silva

  SciPost Phys. Core 6, 051 (2023) · published 18 July 2023 | Toggle abstract · pdf

  We study dynamical phase transitions occurring in the stationary state of the dynamics of integrable many-body non-hermitian Hamiltonians, which can be either realized as a no-click limit of a stochastic Schrödinger equation or using spacetime duality of quantum circuits. In two specific models, the Transverse Field Ising Chain and the Long Range Kitaev Chain, we observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian: bounded entanglement entropy when the imaginary part of the quasi-particle spectrum is gapped and a logarithmic growth for gapless imaginary spectrum. This observation suggests the possibility to generalize the area-law theorem to non-Hermitian Hamiltonians.

  17 citations

• Special transition and extraordinary phase on the surface of a two-dimensional quantum Heisenberg antiferromagnet

  Chengxiang Ding, Wenjing Zhu, Wenan Guo, Long Zhang

  SciPost Phys. 15, 012 (2023) · published 18 July 2023 | Toggle abstract · pdf

  Continuous phase transitions exhibit richer critical phenomena on the surface than in the bulk, because distinct surface universality classes can be realized at the same bulk critical point by tuning the surface interactions. The exploration of surface critical behavior provides a window looking into higher-dimensional boundary conformal field theories. In this work, we study the surface critical behavior of a two-dimensional (2D) quantum critical Heisenberg model by tuning the surface coupling strength, and discover a direct special transition on the surface from the ordinary phase into an extraordinary phase. The extraordinary phase has a long-range antiferromagnetic order on the surface, in sharp contrast to the logarithmic decaying spin correlations in the 3D classical O(3) model. The special transition point has a new set of critical exponents, $y_{s}=0.86(4)$ and $\eta_{\parallel}=-0.33(1)$, which are distinct from the special transition of the classical O(3) model and indicate a new surface universality class of the 3D O(3) Wilson-Fisher theory.

  7 citations