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Andrew Lucas

Publications and source records attributed to Andrew Lucas.

At least 55 records · Page 3Linked to original sources
arXiv2024

Locality bounds for quantum dynamics at low energy

We discuss the generic slowing down of quantum dynamics in low energy density states of spatially local Hamiltonians. Beginning with quantum walks of a single particle, we prove that for certain classes of Hamiltonians (deformations of lattice-regularized $H\propto p^{2k}$), the ``butterfly velocity" of particle motion at low energies has an upper bound that must scale as $E^{(2k-1)/2k}$, as expected from dimensional analysis. We generalize these results to obtain bounds on the typical velocities of particles in many-body systems with repulsive interactions, where for certain families of Hubbard-like models we obtain similar scaling.

math-ph↗
arXiv2024

Heisenberg-limited metrology with perturbing interactions

We show that it is possible to perform Heisenberg-limited metrology on GHZ-like states, in the presence of generic spatially local, possibly strong interactions during the measurement process. An explicit protocol, which relies on single-qubit measurements and feedback based on polynomial-time classical computation, achieves the Heisenberg limit. In one dimension, matrix product state methods can be used to perform this classical calculation, while in higher dimensions the cluster expansion underlies the efficient calculations. The latter approach is based on an efficient classical sampling algorithm for short-time quantum dynamics, which may be of independent interest.

quant-ph↗
arXiv2024

Flux-charge symmetric theory of superconducting circuits

The quantum mechanics of superconducting circuits is derived by starting from a classical Hamiltonian dynamical system describing a dissipationless circuit, usually made of capacitive and inductive elements. However, standard approaches to circuit quantization treat fluxes and charges, which end up as the canonically conjugate degrees of freedom on phase space, asymmetrically. By combining intuition from topological graph theory with a recent symplectic geometry approach to circuit quantization, we present a theory of circuit quantization that treats charges and fluxes on a manifestly symmetric footing. For planar circuits, known circuit dualities are a natural canonical transformation on the classical phase space. We discuss the extent to which such circuit dualities generalize to non-planar circuits.

quant-ph↗
arXiv2023

Generalized time-reversal symmetry and effective theories for nonequilibrium matter

The past decade has witnessed the development of systematic effective theories for dissipative thermal systems. Here, we describe an analogous effective theory framework that applies to the classical stochastic dynamics of nonequilibrium systems. We illustrate this approach using a range of examples, including nonreciprocal (predator-prey) dynamics, dissipative and driven rigid-body motion, and active chiral fluids and solids. Many of these systems exhibit a generalized time-reversal symmetry, which plays a crucial role within our formalism, and in many cases can be implemented within the Martin-Siggia-Rose path integral. This effective theory formalism yields generalizations of the fluctuation-dissipation theorem and second law of thermodynamics valid out of equilibrium. By stipulating a stationary distribution and a set of symmetries -- rather than postulating the stochastic equations of motion directly -- this formalism provides an alternative route to building phenomenological models of driven and active matter. We hope that this approach facilitates a systematic investigation of the universality classes of active matter, and provides a common language for nonequilibrium many-body physics from high energy to condensed matter.

cond-mat.stat-mech↗
arXiv2023

Disordered quantum critical fixed points from holography

Using holographic duality, we present an analytically controlled theory of quantum critical points without quasiparticles, at finite disorder and finite charge density. These fixed points are obtained by perturbing a disorder-free quantum critical point with relevant disorder whose operator dimension is perturbatively close to Harris marginal. We analyze these fixed points both using field theoretic arguments, and by solving the bulk equations of motion in holography. We calculate the critical exponents of the IR theory, together with thermoelectric transport coefficients. Our predictions for the critical exponents of the disordered fixed point are consistent with previous work, both in holographic and nonholograpic models.

cond-mat.str-el↗
arXiv2023

Kinematically constrained vortex dynamics in charge density waves

We build a minimal model of dissipative vortex dynamics in two spatial dimensions, subject to a kinematic constraint: dipole conservation. The additional conservation law implies anomalously slow decay rates for vortices. We argue that this model of vortex dynamics is relevant for a broad range of time scales during a quench into a uniaxial charge density wave state. Our predictions are consistent with recent experiments on uniaxial charge density wave formation in $\mathrm{LaTe}_3$.

cond-mat.stat-mech↗
arXiv2023

Speed limits and locality in many-body quantum dynamics

We review the mathematical speed limits on quantum information processing in many-body systems. After the proof of the Lieb-Robinson Theorem in 1972, the past two decades have seen substantial developments in its application to other questions, such as the simulatability of quantum systems on classical or quantum computers, the generation of entanglement, and even the properties of ground states of gapped systems. Moreover, Lieb-Robinson bounds have been extended in non-trivial ways, to demonstrate speed limits in systems with power-law interactions or interacting bosons, and even to prove notions of locality that arise in cartoon models for quantum gravity with all-to-all interactions. We overview the progress which has occurred, highlight the most promising results and techniques, and discuss some central outstanding questions which remain open. To help bring newcomers to the field up to speed, we provide self-contained proofs of the field's most essential results.

quant-ph↗
arXiv2023

Locality and error correction in quantum dynamics with measurement

The speed of light $c$ sets a strict upper bound on the speed of information transfer in both classical and quantum systems. In nonrelativistic quantum systems, the Lieb-Robinson Theorem imposes an emergent speed limit $v \hspace{-0.2mm} \ll \hspace{-0.2mm} c$, establishing locality under unitary evolution and constraining the time needed to perform useful quantum tasks. We extend the Lieb-Robinson Theorem to quantum dynamics with measurements. In contrast to the expectation that measurements can arbitrarily violate spatial locality, we find at most an $(M \hspace{-0.5mm} +\hspace{-0.5mm} 1)$-fold enhancement to the speed $v$ of quantum information, provided the outcomes of measurements in $M$ local regions are known. This holds even when classical communication is instantaneous, and extends beyond projective measurements to weak measurements and other nonunitary channels. Our bound is asymptotically optimal, and saturated by existing measurement-based protocols. We tightly constrain the resource requirements for quantum computation, error correction, teleportation, and generating entangled resource states (Bell, GHZ, quantum-critical, Dicke, W, and spin-squeezed states) from short-range-entangled initial states. Our results impose limits on the use of measurements and active feedback to speed up quantum information processing, resolve fundamental questions about the nature of measurements in quantum dynamics, and constrain the scalability of a wide range of proposed quantum technologies.

quant-ph↗
arXiv2023

Polynomial-time classical sampling of high-temperature quantum Gibbs states

The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout science, ranging from simulating quantum chemistry to discovering the thermodynamic phase diagram of quantum materials or high-density neutron stars. We present a classical algorithm that samples from a high-temperature quantum Gibbs state in a computational (product state) basis. The runtime grows polynomially with the number of particles, while error vanishes polynomially. This algorithm provides an alternative strategy to existing quantum Monte Carlo methods for overcoming the sign problem. Our result implies that measurement-based quantum computation on a Gibbs state can provide exponential speed up only at sufficiently low temperature, and further constrains what tasks can be exponentially faster on quantum computers.

quant-ph↗
arXiv2023

Non-equilibrium phase transitions in competitive markets caused by network effects

Network effects are the added value derived solely from the popularity of a product in an economic market. Using agent-based models inspired by statistical physics, we propose a minimal theory of a competitive market for (nearly) indistinguishable goods with demand-side network effects, sold by statistically identical sellers. With weak network effects, the model reproduces conventional microeconomics: there is a statistical steady state of (nearly) perfect competition. Increasing network effects, we find a phase transition to a robust non-equilibrium phase driven by the spontaneous formation and collapse of fads in the market. When sellers update prices sufficiently quickly, an emergent monopolist can capture the market and undercut competition, leading to a symmetry- and ergodicity-breaking transition. The non-equilibrium phase simultaneously exhibits three empirically established phenomena not contained in the standard theory of competitive markets: spontaneous price fluctuations, persistent seller profits, and broad distributions of firm market shares.

cond-mat.stat-mech↗
arXiv2023

Prethermalization and the local robustness of gapped systems

We prove that prethermalization is a generic property of gapped local many-body quantum systems, subjected to small perturbations, in any spatial dimension. More precisely, let $H_0$ be a Hamiltonian, spatially local in $d$ spatial dimensions, with a gap $Δ$ in the many-body spectrum; let $V$ be a spatially local Hamiltonian consisting of a sum of local terms, each of which is bounded by $ε\ll Δ$. Then, the approximation that quantum dynamics is restricted to the low-energy subspace of $H_0$ is accurate, in the correlation functions of local operators, for stretched exponential time scale $τ\sim \exp[(Δ/ε)^a]$ for any $a<1/(2d-1)$. This result does not depend on whether the perturbation closes the gap. It significantly extends previous rigorous results on prethermalization in models where $H_0$ was frustration-free. We infer the robustness of quantum simulation in low-energy subspaces, the existence of athermal ``scarred" correlation functions in gapped systems subject to generic perturbations, the long lifetime of false vacua in symmetry broken systems, and the robustness of quantum information in non-frustration-free gapped phases with topological order.

cond-mat.str-el↗
arXiv2023

Symplectic geometry and circuit quantization

Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose degrees of freedom are either magnetic fluxes or electric charges in the circuit. By combining nonlinear circuit elements (such as Josephson junctions or quantum phase slips), it is possible to build circuits where a standard Lagrangian description (and thus the standard quantization method) does not exist. Inspired by the mathematics of symplectic geometry and graph theory, we address this challenge, and present a Hamiltonian formulation of non-dissipative electrodynamic circuits. The resulting procedure for circuit quantization is independent of whether circuit elements are linear or nonlinear, or if the circuit is driven by external biases. We explain how to re-derive known results from our formalism, and provide an efficient algorithm for quantizing circuits, including those that cannot be quantized using existing methods.

quant-ph↗
arXiv2023

Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation

We develop a Schwinger-Keldysh effective field theory describing the hydrodynamics of a fluid with conserved charge and dipole moments, together with conserved momentum. The resulting hydrodynamic modes are highly unusual, including sound waves with quadratic (magnon-like) dispersion relation and subdiffusive decay rate. Hydrodynamics itself is unstable below four spatial dimensions. We show that the momentum density is, at leading order, the Goldstone boson for a dipole symmetry which appears spontaneously broken at finite charge density. Unlike an ordinary fluid, the presence or absence of energy conservation qualitatively changes the decay rates of the hydrodynamic modes. This effective field theory naturally couples to curved spacetime and background gauge fields; in the flat spacetime limit, we reproduce the "mixed rank tensor fields" previously coupled to fracton matter.

hep-th↗
arXiv2023

Analogue viscous current flow near the onset of superconductivity

Spatially resolved transport in two-dimensional quantum materials can reveal dynamics which is invisible in conventional bulk transport measurements. We predict striking patterns in spatially inhomogeneous transport just above the critical temperature in two-dimensional superconducting thin films, where electrical current will appear to flow as if it were a viscous fluid obeying the Navier-Stokes equations. Compared to viscous electron fluids in ultrapure metals such as graphene, this analogue viscous vortex fluid can exhibit a far more tunable crossover, as a function of temperature, from Ohmic to non-Ohmic transport, with the latter arising on increasingly large length scales close to the critical temperature. Experiments using nitrogen vacancy center magnetometry, or transport through patterned thin films, could reveal this analogue viscous flow in a wide variety of materials.

cond-mat.supr-con↗
arXiv2023

Fracton superfluid hydrodynamics

We examine the hydrodynamics of systems with spontaneously broken multipolar symmetries using a systematic effective field theory. We focus on the simplest non-trivial setting: a system with charge and dipole symmetry, but without momentum conservation. When no symmetries are broken, our formalism reproduces the quartic subdiffusion ($ω\sim -i k^4$) characteristic of `fracton hydrodynamics' with conserved dipole moment. Our formalism also captures spontaneous breaking of charge and/or dipole symmetry. When charge symmetry is spontaneously broken, the hydrodynamic modes are quadratically propagating and quartically relaxing ($ω\sim \pm k^2 - ik^4$). When the dipole symmetry is spontaneously broken but the charge symmetry is preserved, then we find quadratically relaxing (diffusive) transverse modes, plus another mode which depending on parameters may be either purely diffusive ($ω\sim -i k^2$) or quadratically propagating and quadratically relaxing ($ω\sim \pm k^2 -i k^2$). Our work provides concrete predictions that may be tested in near-term cold atom experiments, and also lays out a general framework that may be applied to study systems with spontaneously broken multipolar symmetries.

cond-mat.stat-mech↗
arXiv2023

Hydrodynamics with triangular point group

When continuous rotational invariance of a two-dimensional fluid is broken to the discrete, dihedral subgroup $D_6$ - the point group of an equilateral triangle - the resulting anisotropic hydrodynamics breaks both spatial-inversion and time-reversal symmetries, while preserving their combination. In this work, we present the hydrodynamics of such $D_6$ fluids, identifying new symmetry-allowed dissipative terms in the hydrodynamic equations of motion. We propose two experiments - both involving high-purity solid-state materials with $D_6$-invariant Fermi surfaces - that are sensitive to these new coefficients in a $D_6$ fluid of electrons. In particular, we propose a local current imaging experiment (which is present-day realizable with nitrogen vacancy center magnetometry) in a hexagonal device, whose $D_6$-exploiting boundary conditions enable the unambiguous detection of these novel transport coefficients.

cond-mat.str-el↗
arXiv2022

Anomalous hydrodynamics with triangular point group in 2 + 1 dimensions

We present a theory of hydrodynamics for a vector U(1) charge in 2+1 dimensions, whose rotational symmetry is broken to the point group of an equilateral triangle. We show that it is possible for this U(1) to have a chiral anomaly. The hydrodynamic consequence of this anomaly is the introduction of a ballistic contribution to the dispersion relation for the hydrodynamic modes. We simulate classical Markov chains and find compelling numerical evidence for the anomalous hydrodynamic universality class. Generalizations of our theory to other symmetry groups are also discussed.

cond-mat.stat-mech↗
arXiv2022

Hydrodynamics with helical symmetry

We present the hydrodynamics of fluids in three spatial dimensions with helical symmetry, wherein only a linear combination of a rotation and translation is conserved in one of the three directions. The hydrodynamic degrees of freedom consist of scalar densities (e.g. energy or charge) along with two velocity fields transverse to the helical axis when the corresponding momenta are conserved. Nondissipative hydrodynamic coefficients reminiscent of chiral vortical coefficients arise. We write down microscopic Hamiltonian dynamical systems exhibiting helical symmetry, and we demonstrate using kinetic theory that these systems will generically exhibit the new helical phenomena that we predicted within hydrodynamics. We also confirm our findings using modern effective field theory techniques for hydrodynamics. We postulate regimes where pinned cholesteric liquid crystals may possess transport coefficients of a helical fluid, which appear to have been overlooked in previous literature.

cond-mat.stat-mech↗