Publications

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Non-equilibrium Sachdev-Ye-Kitaev model with quadratic perturbation

Aleksey V. Lunkin, Mikhail V. Feigel’man

SciPost Phys. 12, 031 (2022) · published 20 January 2022 | · pdf

We consider a non-equilibrium generalization of the mixed SYK$_4$+SYK$_2$ model and calculate the energy dissipation rate $W(\omega)$ that results due to periodic modulation of random quadratic matrix elements with a frequency $\omega$. We find that $W(\omega)$ possesses a peak at $\omega$ close to the polaron energy splitting $\omega_R$ found recently (PRL 125, 196602), demonstrating the physical significance of this energy scale. Next, we study the effect of energy pumping with a finite amplitude at the resonance frequency $\omega_R$ and calculate, in presence of this pumping, non-equilibrium dissipation rate due to low-frequency parametric modulation. We found an unusual phenomenon similar to "dry friction" in presence of pumping.

2 citations
High-frequency transport and zero-sound in an array of SYK quantum dots

Aleksey. V. Lunkin, Mikhail . V. Feigel'man

SciPost Phys. 13, 073 (2022) · published 29 September 2022 | · pdf

We study an array of strongly correlated quantum dots of complex SYK type and account for the effects of quadratic terms added to the SYK Hamiltonian; both local terms and inter-dot tunneling are considered in the non-Fermi-liquid temperature range $T \gg T_{FL}$. We take into account soft-mode fluctuations and demonstrate their relevance for physical observables. Electric $\sigma(\omega,p)$ and thermal $\kappa(\omega,p)$ conductivities are calculated as functions of frequency and momentum for arbitrary values of the particle-hole asymmetry parameter $\mathcal{E}$. At low-frequencies $\omega \ll T$ we find the Lorenz ratio $L = \kappa(0,0)/T\sigma(0,0)$ to be non-universal and temperature-dependent. At $\omega \gg T$ the conductivity $\sigma(\omega,p)$ contains a pole with nearly linear dispersion $\omega \approx sp\sqrt{\ln\frac{\omega}{T}}$ reminiscent of the "zero-sound", known for Fermi-liquids. We demonstrate also that the developed approach makes it possible to understand the origin of heavy Fermi liquids with anomalously large Kadowaki-Woods ratio.

2 citations
Quantum analytic Langlands correspondence

Davide Gaiotto, Jörg Teschner

SciPost Phys. 18, 144 (2025) · published 30 April 2025 | · pdf

The analytic Langlands correspondence describes the solution to the spectral problem for the quantised Hitchin Hamiltonians. It is related to the S-duality of $\mathcal{N}=4$ super Yang-Mills theory. We propose a one-parameter deformation of the Analytic Langlands Correspondence, and discuss its relations to quantum field theory. The partition functions of the $H_3^+$ WZNW model are interpreted as the wave-functions of a spherical vector in the quantisation of complex Chern-Simons theory. Verlinde line operators generate a representation of two copies of the quantised skein algebra on generalised partition functions. We conjecture that this action generates a basis for the underlying Hilbert space, and explain in which sense the resulting quantum theory represents a deformation of the Analytic Langlands Correspondence.

2 citations
Fermi-liquid corrections to the intrinsic anomalous Hall conductivity of topological metals

Ivan Pasqua, Michele Fabrizio

SciPost Phys. 19, 014 (2025) · published 16 July 2025 | · pdf

We show that topological metals lacking time-reversal symmetry have an intrinsic non-quantised component of the anomalous Hall conductivity which is contributed not only by the Berry phase of quasiparticles on the Fermi surface, but also by Fermi-liquid corrections due to the residual interactions among quasiparticles, the Landau $f$-parameters. These corrections pair up with those that modify the optical mass with respect to the quasiparticle effective one, or the charge compressibility with respect to the quasiparticle density of states. Our result supports recent claims that the correct expressions for topological observables include vertex corrections besides the topological invariants built just upon the Green's functions. Furthermore, it demonstrates that such corrections are naturally accounted for by Landau's Fermi liquid theory, here extended to the case in which coherence effects between bands crossing the chemical potential and those that are instead away from it may play a crucial role, as in the anomalous Hall conductivity, and have important implications when those metals are on the verge of a doping-driven Mott transition, as we discuss.

2 citations
Joule heating in bad and slow metals

Paolo Glorioso, Sean A. Hartnoll

SciPost Phys. 13, 095 (2022) · published 12 October 2022 | · pdf

Heat supplied to a metal is absorbed by the electrons and then transferred to the lattice. In conventional metals energy is released to the lattice by phonons emitted from the Lindhard continuum. However in a 'bad' metal, with short mean free path, the low energy Lindhard continuum is destroyed. Furthermore in a 'slow' metal, with Fermi velocity less than the sound velocity, particle-hole pairs are kinematically unable to emit phonons. To describe energy transfer to the lattice in these cases we obtain a general Kubo formula for the energy relaxation rate in terms of the electronic density spectral weight $\text{Im} \, G^R_{nn}(\omega_k,k)$ evaluated on the phonon dispersion $\omega_k$. We apply our Kubo formula to the high temperature Hubbard model, using recent data from quantum Monte Carlo and experiments in ultracold atoms to characterize $\text{Im} \, G^R_{nn}(\omega_k,k)$. We furthermore use recent data from electron energy-loss spectroscopy to estimate the energy relaxation rate of the cuprate strange metal to a high energy optical phonon. As a second, distinct, application of our formalism we consider 'slow' metals. These are defined to have Fermi velocity less than the sound velocity, so that particle-hole pairs are kinematically unable to emit phonons. We obtain an expression for the energy relaxation rate of a slow metal in terms of the optical conductivity.

2 citations
U(1) gauging, continuous TQFTs, and higher symmetry structures

Adrien Arbalestrier, Riccardo Argurio, Luigi Tizzano

SciPost Phys. 19, 032 (2025) · published 12 August 2025 | · pdf

Quantum field theories can exhibit various generalized symmetry structures, among which higher-group symmetries and non-invertible symmetry defects are particularly prominent. In this work, we explore a new general scenario in which these two structures are intertwined. This phenomenon arises in four dimensions when gauging one of multiple $U(1)$ 0-form symmetries in the presence of mixed 't Hooft anomalies. We illustrate this with two distinct models that flow to an IR gapless phase and a gapped phase, respectively, and examine how this symmetry structure manifests in each case. Additionally, we investigate a five-dimensional model where a similar structure exists intrinsically. Our main tool is a symmetry TQFT in one higher dimension, formulated using non-compact gauge fields and having infinitely many topological operators. We carefully determine its boundary conditions and provide a detailed discussion on various dressing choices for its bulk topological operators.

2 citations
Precision magnetometry exploiting excited state quantum phase transitions

Qian Wang, Ugo Marzolino

SciPost Phys. 17, 043 (2024) · published 9 August 2024 | · pdf

Critical behaviour in phase transitions is a resource for enhanced precision metrology. The reason is that the function, known as Fisher information, is superextensive at critical points, and, at the same time, quantifies performances of metrological protocols. Therefore, preparing metrological probes at phase transitions provides enhanced precision in measuring the transition control parameter. We focus on the Lipkin-Meshkov-Glick model that exhibits excited state quantum phase transitions at different magnetic fields. Resting on the model spectral properties, we show broad peaks of the Fisher information, and propose efficient schemes for precision magnetometry. The Lipkin-Meshkov-Glick model was first introduced for superconductivity and for nuclear systems, and recently realised in several condensed matter platforms. The above metrological schemes can be also exploited to measure microscopic properties of systems able to simulate the Lipkin-Meshkov-Glick model.

2 citations
Importance sampling scheme for the stochastic simulation of quantum spin dynamics

Stefano De Nicola

SciPost Phys. 11, 048 (2021) · published 2 September 2021 | · pdf

The numerical simulation of dynamical phenomena in interacting quantum systems is a notoriously hard problem. Although a number of promising numerical methods exist, they often have limited applicability due to the growth of entanglement or the presence of the so-called sign problem. In this work, we develop an importance sampling scheme for the simulation of quantum spin dynamics, building on a recent approach mapping quantum spin systems to classical stochastic processes. The importance sampling scheme is based on identifying the classical trajectory that yields the largest contribution to a given quantum observable. An exact transformation is then carried out to preferentially sample trajectories that are close to the dominant one. We demonstrate that this approach is capable of reducing the temporal growth of fluctuations in the stochastic quantities, thus extending the range of accessible times and system sizes compared to direct sampling. We discuss advantages and limitations of the proposed approach, outlining directions for further developments.

2 citations
The sky remembers everything: Celestial amplitude, shadow and OPE in quadratic EFT of gravity

Arpan Bhattacharyya, Saptaswa Ghosh, Sounak Pal

SciPost Phys. 19, 041 (2025) · published 15 August 2025 | · pdf

In this paper, we compute the celestial amplitude arising from higher curvature corrections to Einstein gravity, incorporating phase dressing. The inclusion of such corrections leads to effective modifications of the theory's ultraviolet (UV) behaviour. In the eikonal limit, we find that, in contrast to Einstein's gravity, where the $u$ and $s$-channel contributions cancel, these contributions remain non-vanishing in the presence of higher curvature terms. We examine the analytic structure of the resulting amplitude and derive a dispersion relation for the phase-dressed eikonal amplitude in quadratic gravity. Furthermore, we investigate the celestial conformal block expansion of the Mellin-transformed conformal shadow amplitude within the framework of celestial conformal field theory (CCFT). As a consequence, we compute the corresponding operator product expansion (OPE) coefficients using the Burchnall-Chaundy expansion. In addition, we evaluate the OPE via the Euclidean OPE inversion formula across various kinematic channels and comment on its applicability and implications. Finally, we briefly explore the Carrollian amplitude associated with the corresponding quadratic EFT.

2 citations
Flat bands and compact localised states: A Carrollian roadmap

Nisa Ara, Aritra Banerjee, Rudranil Basu, Bhagya Krishnan

SciPost Phys. 19, 046 (2025) · published 19 August 2025 | · pdf

We show how Carrollian symmetries become important in the construction of one-dimensional fermionic systems with all flat-band spectra from first principles. The key ingredient of this construction is the identification of Compact Localised States (CLSs), which appear naturally by demanding supertranslation invariance of the system. We use CLS basis states, with inherent ultra-local correlations, to write down an interacting theory which shows a non-trivial phase structure and an emergent Carroll conformal symmetry at the gapless points. We analyze this theory in detail for both zero and finite chemical potential.

2 citations

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