arXiv subjects

Luca V. Delacrétaz

Publications and source records attributed to Luca V. Delacrétaz.

At least 19 recordsLinked to original sources

arXiv2026

Theory of Out-of-Time-Ordered Transport

We construct an effective field theory (EFT) that captures the universal behavior of out-of-time-order correlators (OTOCs) at late times in generic quantum many-body systems with conservation laws. The EFT hinges on a generalization of the strong-to-weak spontaneous symmetry breaking pattern adapted to out-of-time-order observables, and reduces to conventional fluctuating hydrodynamics when time-ordered observables are probed. We use the EFT to explain different power-law behavior observed in OTOCs at late times, and show that many OTOCs are entirely fixed by conventional transport data at leading order. Nevertheless, we show that a specific combination of OTOCs is sensitive to novel transport parameters, not visible in regular time-ordered correlators. We test our predictions in Hamiltonian and Floquet spin chains in one spatial dimension.

cond-mat.str-el↗

arXiv2026

Quantum Critical Solids

We study the fate of quantum solids with a vanishing velocity of transverse phonons. Such ``floppy'' solids exhibit a cubic elastic nonlinearity that is relevant in spatial dimensions $d<4$ and drives the system to a strongly-coupled Lifshitz quantum critical point in $d=3$, that we analyze in an $ε= 4-d$ expansion. The associated phase transition is generically first-order, preempting the system's full access to the strongly-coupled fixed point. Nevertheless, the critical data of this quantum critical point is accessible within a Ginzburg region in the vicinity of the transition. This cubic nonlinearity vanishes exactly in $d=2$, where the leading interactions are instead quartic and are marginal, leading to weak logarithmic singularities. We discuss possible realizations of this ``crystal Lifshitz criticality'' in quantum materials.

cond-mat.str-el↗

arXiv2026

Eigenstate Thermalization Hypothesis correlations via non-linear Hydrodynamics

The thermalizing dynamics of many-body systems is often described through the lens of the Eigenstate Thermalization Hypothesis (ETH). ETH postulates that the statistical properties of observables, when expressed in the energy eigenbasis, are described by smooth functions, that also describe correlations among the matrix elements. However, the form of these functions is usually left undetermined, constituting a key missing component of the ETH framework. In this work, we investigate the structure of such smooth functions by focusing on their Fourier transform, recently identified as free cumulants. Using non-linear hydrodynamics, we provide a prediction for the universal scaling of the late-time behavior of time-ordered free cumulants in the thermodynamic limit. The prediction is further corroborated by large-scale numerical simulations of several non-integrable one-dimensional spin models which exhibit diffusive transport behavior. Good agreement is observed in both infinite and finite-temperature regimes and for a collection of local observables. Our results indicate that the smooth multi-point correlation functions within the ETH framework admit a universal hydrodynamic description at low frequencies.

cond-mat.stat-mech↗

arXiv2025

Symmetry and causality constraints on Fermi liquids

We investigate symmetry and causality constraints on interacting Fermi liquids. Whereas Galilean or Lorentz boost symmetry leads to a well-known constraint on the first Landau parameter $F_1$, we show that scale invariance similarly constrains $F_0$. In the case of conformal Fermi liquids, we show that causality constraints on the particle-hole continuum and on zero sound strongly restrict the available parameter space for interacting Fermi liquids. We also consider nonlinear response, which we show is sensitive to additional ``generalized Landau parameters'' even at lowest orders in the long wavelength limit. We impose Galilean, Lorentz and scale symmetry on these generalized Landau parameters, obtaining further nonlinear constraints. We test our constraints in several microscopic models that enter a Fermi liquid phase.

hep-th↗

arXiv2025

Hilbert Space Diffusion in Systems with Approximate Symmetries

Random matrix theory (RMT) universality is the defining property of quantum mechanical chaotic systems, and can be probed by observables like the spectral form factor (SFF). In this paper, we describe systematic deviations from RMT behaviour at intermediate time scales in systems with approximate symmetries. At early times, the symmetries allow us to organize the Hilbert space into approximately decoupled sectors, each of which contributes independently to the SFF. At late times, the SFF transitions into the final ramp of the fully mixed chaotic Hamiltonian. For approximate continuous symmetries, the transitional behaviour is governed by a universal process that we call Hilbert space diffusion. The diffusion constant corresponding to this process is related to the relaxation rate of the associated nearly conserved charge. By implementing a chaotic sigma model for Hilbert-space diffusion, we formulate an analytic theory of this process which agrees quantitatively with our numerical results for different examples.

cond-mat.stat-mech↗

arXiv2024

Corrections to diffusion in interacting quantum systems

Transport and the approach to equilibrium in interacting classical and quantum systems is a challenging problem of both theoretical and experimental interest. One useful organizing principle characterizing equilibration is the dissipative universality class, the most prevalent one being diffusion. In this paper, we use the effective field theory (EFT) of diffusion to systematically obtain universal power-law corrections to diffusion. We then employ large-scale simulations of classical and quantum systems to explore their validity. In particular, we find universal scaling functions for the corrections to the dynamical structure factor $\langle n(x,t)n\rangle$, in the presence of a single $U(1)$ or $SU(2)$ charge in systems with and without particle-hole symmetry, and present the framework to generalize the calculation to multiple charges. Classical simulations show remarkable agreement with EFT predictions for subleading corrections, pushing precision tests of effective theories for thermalizing systems to an unprecedented level. Moving to quantum systems, we perform large-scale tensor-network simulations in unitary and noisy 1d Floquet systems with conserved magnetization. We find a qualitative agreement with EFT which becomes quantitative in the case of noisy systems. Additionally, we show how the knowledge of EFT corrections allows for fitting methods, which can improve the estimation of transport parameters at the intermediate times accessible by simulations and experiments. Finally, we explore non-linear response in quantum systems and find that EFT provides an accurate prediction for its behavior. Our results provide a basis for a better understanding of the non-linear phenomena present in thermalizing systems.

cond-mat.stat-mech↗

arXiv2023

Conformal field theories in a magnetic field

We study the properties of 2+1d conformal field theories (CFTs) in a background magnetic field. Using generalized particle-vortex duality, we argue that in many cases of interest the theory becomes gapped, which allows us to make a number of predictions for the magnetic response, background monopole operators, and more. Explicit calculations at large N for Wilson-Fisher and Gross-Neveu CFTs support our claim, and yield the spectrum of background (defect) monopole operators. Finally, we point out that other possibilities exist: certain CFTs can become metallic in a magnetic field. Such a scenario occurs for a Dirac fermion coupled to a Chern-Simons gauge field, where a non-Fermi liquid is argued to emerge.

hep-th↗

arXiv2022

Damping of Pseudo-Goldstone Fields

Approximate symmetries abound in Nature. If these symmetries are also spontaneously broken, the would-be Goldstone modes acquire a small mass, or inverse correlation length, and are referred to as pseudo-Goldstones. At nonzero temperature, the effects of dissipation can be captured by hydrodynamics at sufficiently long scales compared to the local equilibrium. Here we show that in the limit of weak explicit breaking, locality of hydrodynamics implies that the damping of pseudo-Goldstones is completely determined by their mass and diffusive transport coefficients. We present many applications: superfluids, QCD in the chiral limit, Wigner crystal and density wave phases in the presence of an external magnetic field or not, nematic phases and (anti-)ferromagnets. For electronic density wave phases, pseudo-Goldstone damping generates a contribution to the resistivity independent of the strength of disorder, which can have a linear temperature dependence provided the associated diffusivity saturates a bound. This is reminiscent of the phenomenology of strange metal high $T_c$ superconductors, where charge density waves are observed across the phase diagram.

hep-th↗

arXiv2020

Hydrodynamics in lattice models with continuous non-Abelian symmetries

We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models with continuous non-Abelian symmetries are ubiquitous in physics, arising in diverse settings ranging from hot nuclear matter to cold atomic gases and quantum spin chains. In every dimension and for every flavor symmetry group, the low energy theory is a set of coupled noisy diffusion equations. Independence of the physics on the choice of canonical or microcanonical ensemble is manifest in our hydrodynamic expansion, even though the ensemble choice causes an apparent shift in quasinormal mode spectra. We use our formalism to explain why flavor symmetry is qualitatively different from hydrodynamics with other non-Abelian conservation laws, including angular momentum and charge multipoles. As a significant application of our framework, we study spin and energy diffusion in classical one-dimensional SU(2)-invariant spin chains, including the Heisenberg model along with multiple generalizations. We argue based on both numerical simulations and our effective field theory framework that non-integrable spin chains on a lattice exhibit conventional spin diffusion, in contrast to some recent predictions that diffusion constants grow logarithmically at late times. We show that the apparent enhancement of diffusion is due to slow equilibration caused by (non-Abelian) hydrodynamic fluctuations.

cond-mat.stat-mech↗

arXiv2020

Superfluids as Higher-form Anomalies

We recast superfluid hydrodynamics as the hydrodynamic theory of a system with an emergent anomalous higher-form symmetry. The higher-form charge counts the winding planes of the superfluid -- its constitutive relation replaces the Josephson relation of conventional superfluid hydrodynamics. This formulation puts all hydrodynamic equations on equal footing. The anomalous Ward identity can be used as an alternative starting point to prove the existence of a Goldstone boson, without reference to spontaneous symmetry breaking. This provides an alternative characterization of Landau phase transitions in terms of higher-form symmetries and their anomalies instead of how the symmetries are realized. This treatment is more general and, in particular, includes the case of BKT transitions. As an application of this formalism we construct the hydrodynamic theories of conventional (0-form) and 1-form superfluids.

hep-th↗

arXiv2019

Theory of diffusive fluctuations

The recently developed effective field theory of fluctuations around thermal equilibrium is used to compute late-time correlation functions of conserved densities. Specializing to systems with a single conservation law, we find that the diffusive pole is shifted in the presence of non-linear hydrodynamic self-interactions, and that the density-density Green's function acquires a branch point half way to the diffusive pole, at frequency $ω= -\frac{i}{2}Dk^2$. We discuss the relevance of diffusive fluctuations for strongly correlated transport in condensed matter and cold atomic systems.

hep-th↗

arXiv2019

Theory of the collective magnetophonon resonance and melting of the field-induced Wigner solid

Electron solid phases of matter are revealed by characteristic vibrational resonances. Sufficiently large magnetic fields can overcome the effects of disorder, leading to a weakly pinned collective mode called the magnetophonon. Consequently, in this regime it is possible to develop a tightly constrained hydrodynamic theory of pinned magnetophonons. The behavior of the magnetophonon resonance across thermal and quantum melting transitions has been experimentally characterized in two-dimensional electron systems. Applying our theory to these transitions we explain several key features of the data: (i) violation of the Fukuyama-Lee sum rule as the transition is approached is directly tied to the non-Lorentzian form taken by the resonance and (ii) the non-Lorentzian shape is caused by characteristic dissipative channels that become especially important close to melting: proliferating dislocations and uncondensed charge carriers.

cond-mat.mes-hall↗

arXiv2018

Conformal Truncation of Chern-Simons Theory at Large $N_f$

We set up and analyze the lightcone Hamiltonian for an abelian Chern-Simons field coupled to $N_f$ fermions in the limit of large $N_f$ using conformal truncation, i.e. with a truncated space of states corresponding to primary operators with dimension below a maximum cutoff $Δ_{\rm max}$. In both the Chern-Simons theory, and in the $O(N)$ model at infinite $N$, we compute the current spectral functions analytically as a function of $Δ_{\rm max}$ and reproduce previous results in the limit that the truncation $Δ_{\rm max}$ is taken to $\infty$. Along the way, we determine how to preserve gauge invariance and how to choose an optimal discrete basis for the momenta of states in the truncation space.

hep-th↗

arXiv2018

Thermalization, Viscosity and the Averaged Null Energy Condition

We explore the implications of the averaged null energy condition for thermal states of relativistic quantum field theories. A key property of such thermal states is the thermalization length. This lengthscale generalizes the notion of a mean free path beyond weak coupling, and allows finite size regions to independently thermalize. Using the eigenstate thermalization hypothesis, we show that thermal fluctuations in finite size `fireballs' can produce states that violate the averaged null energy condition if the thermalization length is too short or if the shear viscosity is too large. These bounds become very weak with a large number N of degrees of freedom but can constrain real-world systems, such as the quark-gluon plasma.

hep-th↗

arXiv2018

Theory of the supercyclotron resonance and Hall response in anomalous 2d metals

Weakly disordered superconducting films can be driven into an anomalous low temperature resistive state upon applying a magnetic field. Recent experiments on weakly disordered amorphous InO$_x$ have established that both the Hall resistivity and the frequency of a cyclotron-like resonance in the anomalous metal are highly suppressed relative to the values expected for a conventional metal. We show that both of these observations can be understood from the flux flow dynamics of vortices in a superconductor with significant vortex pinning. Results for flux flow transport are obtained using a systematic hydrodynamic expansion, controlled by the diluteness of mobile vortices at low temperatures. Hydrodynamic transport coefficients are related to microscopics through Kubo formulae for the longitudinal and Hall vortex conductivities, as well as a `vorto-electric' conductivity.

cond-mat.supr-con↗

arXiv2017

Theory of hydrodynamic transport in fluctuating electronic charge density wave states

We describe the collective hydrodynamic motion of an incommensurate charge density wave state in a clean electronic system. Our description simultaneously incorporates the effects of both pinning due to weak disorder and also phase relaxation due to proliferating dislocations. We show that the interplay between these two phenomena has important consequences for charge and momentum transport. For instance, it can lead to metal-insulator transitions. We furthermore identify signatures of fluctuating density waves in frequency and spatially resolved conductivities. Phase disordering is well known to lead to a large viscosity. We derive a precise formula for the phase relaxation rate in terms of the viscosity in the dislocation cores. We thereby determine the viscosity of the superconducting state of BSCCO from the observed melting dynamics of Abrikosov lattices and show that the result is consistent with dissipation into Bogoliubov quasiparticles.

cond-mat.str-el↗

arXiv2017

Bad Metals from Fluctuating Density Waves

Bad metals have a large resistivity without being strongly disordered. In many bad metals the Drude peak moves away from zero frequency as the resistivity becomes large at increasing temperatures. We catalogue the position and width of the `displaced Drude peak' in the observed optical conductivity of several families of bad metals, showing that $ω_\text{peak} \sim Δω\sim k_BT/\hbar$. This is the same quantum critical timescale that underpins the $T$-linear dc resistivity of many of these materials. We provide a unified theoretical description of the optical and dc transport properties of bad metals in terms of the hydrodynamics of short range quantum critical fluctuations of incommensurate density wave order. Within hydrodynamics, pinned translational order is essential to obtain the nonzero frequency peak.

cond-mat.str-el↗

arXiv2017

Hydrodynamic theory of quantum fluctuating superconductivity

A hydrodynamic theory of transport in quantum mechanically phase-disordered superconductors is possible when supercurrent relaxation can be treated as a slow process. We obtain general results for the frequency-dependent conductivity of such a regime. With time-reversal invariance, the conductivity is characterized by a Drude-like peak, with width given by the supercurrent relaxation rate. Using the memory matrix formalism, we obtain a formula for this width (and hence also the dc resistivity) when the supercurrent is relaxed by short range Coulomb interactions. This leads to a new -- effective field theoretic and fully quantum -- derivation of a classic result on flux flow resistance. With strong breaking of time-reversal invariance, the optical conductivity exhibits what we call a `hydrodynamic supercyclotron' resonance. We obtain the frequency and decay rate of this resonance for the case of supercurrent relaxation due to an emergent Chern-Simons gauge field. The supercurrent decay rate in this `topologically ordered superfluid vortex liquid' is determined by the conductivities of the normal component of the liquid. Our work gives a controlled framework for low temperature metallic phases arising from phase-disordered superconductivity.

cond-mat.supr-con↗