Goldstone Mode Research Articles

Elastic properties and thermodynamic anomalies of supersolids

We study a supersolid in the context of a Gross-Pitaevskii theory with a nonlocal effective potential. We employ a homogenization technique which allows us to calculate the elastic moduli, supersolid fraction, and other state variables of the system. Our methodology is verified against numerical simulations of elastic deformations. We can also verify that the long-wavelength Goldstone modes that emerge from this technique agree with Bogoliubov theory. We find a thermodynamic anomaly that the supersolid does not obey the thermodynamic relation ∂P/∂V|N=−n(∂P/∂N|V), which we claim is a feature unique to supersolids. Published by the American Physical Society 2024

Nambu–Goldstone modes in a lattice Nambu–Jona-Lasinio model with multi flavor symmetries

Nambu–Goldstone modes in a lattice Nambu–Jona-Lasinio model with multi flavor symmetries

Impossible symmetries and conformal gravity

We explore the physics of relativistic gapless phases defined by a mixed anomaly between two generalized conserved currents. The gapless modes can be understood as Goldstone modes arising from the nonlinear realization of (generically higher-form) symmetries arising from these currents. In some cases, the anomaly cannot be reproduced by any local and unitary theory, indicating that the corresponding symmetries are impossible, in the sense that they cannot appear in a Lorentzian physical system. We give a general construction and illustrate it with several examples. Most notably, we study conformal gravity from this perspective, describing the higher-form symmetries of the linear theory and showing how it can be understood in terms of anomalies. Along the way we clarify some aspects of electric-magnetic duality in linear conformal gravity. Published by the American Physical Society 2024

Probing the impact of bent-core mesogen on the dielectric relaxations of ferroelectric liquid crystal

The modulation in dielectric relaxations of a conventional ferroelectric liquid crystal (FLC, SCE9) material by doping the bent-core mesogen (BCM) derived from the oxadiazole bisaniline moiety has been greatly investigated using frequency-temperature dependent dielectric spectroscopy. The application of probing ac voltage (i.e., oscillating voltage, 800 mV) has clearly shown the presence of partially unwound helical mode (p-UHM) along with Goldstone mode (GM). However, the temperature-dependent dielectric studies further demonstrate that p-UHM gets merged with GM at higher temperatures and hence becomes difficult to observe it separately. It appears that doping of BCM into FLC leads to the suppression of p-UHM at lower temperature, but with the increase in the concentration of dopant beyond a certain point, p-UHM mode reappears. Moreover, the significant decrement (∼9 °C) in SmC*-SmA* phase transition temperature of FLC with increase in the dopant BCM concentration up to 3 wt%. We believe that such studies would be certainly useful for the understanding of the plausible interaction between two different shaped mesogens (i.e., rod and bent-core) present in the mixture and could pave the way forward to the use of one type of mesogen in the modulation of the dielectric properties of other mesogen.

Dynamic Scaling of Two-Dimensional Polar Flocks.

We propose a hydrodynamic description of the homogeneous ordered phase of polar flocks. Starting from symmetry principles, we construct the appropriate equation for the dynamics of the Goldstone mode associated with the broken rotational symmetry. We then focus on the two-dimensional case considering both "Malthusian flocks" for which the density field is a fast variable that does not enter the hydrodynamic description and "Vicsek flocks" for which it does. In both cases, we argue in favor of scaling relations that allow one to compute exactly the scaling exponents, which are found in excellent agreement with previous simulations of the Vicsek model and with the numerical integration of our hydrodynamic equations.

Non-analyticity of the S-matrix with spontaneously broken Lorentz invariance

We study the S-matrix of Goldstones in the renormalizable theory of a U(1) complex scalar at finite charge, i.e. in a state that breaks Lorentz invariance. The theory is weakly coupled so that this S-matrix exists at all energies. Unlike the Lorentz invariant case, the resulting S-matrix is not analytic in the exchanged (complexified) four-momentum. The non-analyticities stem from the LSZ reduction formula, as a consequence of the energy-dependent mixing between the radial and Goldstone modes.

Universal Phenomenology at Critical Exceptional Points of Nonequilibrium O(N) Models

In thermal equilibrium the dynamics of phase transitions is largely controlled by fluctuation-dissipation relations: On the one hand, friction suppresses fluctuations, while on the other hand, the thermal noise is proportional to friction constants. Out of equilibrium, this balance dissolves and one can have situations where friction vanishes due to antidamping in the presence of a finite noise level. We study a wide class of O(N) field theories where this situation is realized at a phase transition, which we identify as a critical exceptional point. In the ordered phase, antidamping induces a continuous limit cycle rotation of the order parameter with an enhanced number of 2N−3 Goldstone modes. Close to the critical exceptional point, however, fluctuations diverge so strongly due to the suppression of friction that in dimensions d<4 they universally either destroy a preexisting static order or give rise to a fluctuation-induced first-order transition. This is demonstrated within a full resummation of loop corrections via Dyson-Schwinger equations for N=2, and a generalization for arbitrary N, which can be solved in the long wavelength limit. We show that in order to realize this physics it is not necessary to drive a system far out of equilibrium: Using the peculiar protection of Goldstone modes, the transition from an xy magnet to a ferrimagnet is governed by an exceptional critical point once weakly perturbed away from thermal equilibrium. Published by the American Physical Society 2024

Gravitational wave analogs in spin nematics and cold atoms

Large-scale gravitational phenomena are famously difficult to observe, making parallels in condensed matter physics a valuable resource. Here we show how spin nematic phases, found in magnets and cold atoms, can provide an analog to linearized gravity. In particular, we show that the Goldstone modes of these systems are massless spin-2 bosons, in one-to-one correspondence with quantized gravitational waves in flat spacetime. We identify a spin-1 model supporting these excitations and, using simulation, outline a procedure for their observation in a 23Na spinor condensate. Published by the American Physical Society 2024

Linear and Nonlinear Electro-optic Response of MHPOCBC

This study investigated the linear and second-order electro-optic responses in chiral smectic liquid crystal 4-(1-methylheptyloxycarbonyl) phenyl 4-octylcarbonyloxybiphenyl-4-carboxylate (MHPOCBC). The result revealed a single Debye-type relaxation in the linear electro-optic frequency dispersion, with a relaxation frequency extending up to one hundred kHz. Conversely, the second-order electro-optic response exhibited intricate temperature-dependence, accurately depicted by a phenomenological Landau theory around the SmA–SmCa* phase transition point. Notably, in the SmCa* phase, critical slowing down of the amplitude mode occurred near the transition to the SmA phase, while at lower temperatures of the SmCa* phase, a distinct low-frequency relaxation mode emerged. Furthermore, the relaxation frequency of the antiferroelectric Goldstone mode in the SmCA* phase remained constant across the entire temperature range. These findings should significantly contribute to the understanding of dynamic behaviors in chiral smectic liquid crystals, shedding light on their complex phase transitions and electro-optic properties.

Hybrid Goldstone Modes from the Double Copy Bootstrap

We perform a systematic classification of scalar field theories whose amplitudes admit a double copy formulation and identify two building blocks at four-point and 13 at five-point. Using the four-point blocks simultaneously as bootstrap seeds, this naturally leads to a single copy theory that is a gauged nonlinear sigma model. Moreover, its double copy includes a novel theory that can be written in terms of Lovelock invariants of an induced metric, and includes Dirac-Born-Infeld and the special Galileon in specific limits. The amplitudes of these Goldstone modes have two distinct soft behavior regimes, corresponding to a hybrid of nonlinear symmetries. Published by the American Physical Society 2024

Critical Casimir effect in a disordered O(2)-symmetric model.

The critical Casimir effect appears when critical fluctuations of an order parameter interact with classical boundaries. We investigate this effect in the setting of a Landau-Ginzburg model with continuous symmetry in the presence of quenched disorder. The quenched free energy is written as an asymptotic series of moments of the model's partition function. Our main result is that, in the presence of a strong disorder, Goldstone modes of the system contribute either with either an attractive or a repulsive force. This result was obtained using the distributional zeta-function method without relying on any particular ansatz in the functional space of the moments of the partition function.

Nonequilibrium Criticality at the Onset of Time-Crystalline Order.

We explore the phase transitions at the onset of time-crystalline order in O(N) models driven out of equilibrium. The spontaneous breaking of time translation symmetry and its Goldstone mode are captured by an effective description with O(N)×SO(2) symmetry, where the emergent external SO(2) results from a transmutation of the internal symmetry of time translations. Using the renormalization group and the ε=4-d expansion in a leading two-loop analysis, we identify a new nonequilibrium universality class. Strikingly, it controls the long-distance physics no matter how small the microscopic breaking of equilibrium conditions is. The O(N=2)×SO(2) symmetry group is realized for magnon condensation in pumped yttrium iron garnet films and in exciton-polariton systems with a polarization degree of freedom.

Sound, Superfluidity, and Layer Compressibility in a Ring Dipolar Supersolid.

We propose a protocol to excite the Goldstone modes of a supersolid dipolar Bose-Einstein condensed gas confined in a ring geometry. By abruptly removing an applied periodic modulation proportional to cos(φ), where φ is the azimuthal angle, we explore the resulting oscillations of the gas by solving the extended Gross-Pitaevskii equation. The value of the two longitudinal sound velocities exhibited in the supersolid phase are analyzed using the hydrodynamic theory of supersolids at zero temperature, which explicitly takes into account both the superfluid and the crystal nature of the system. This approach allows for the determination of the layer compressibility modulus as well as of the superfluid fraction, f_{S}, in agreement with the Leggett estimate of the nonclassical moment of inertia.

Friction of a driven chain: role of momentum conservation, Goldstone and radiation modes

We analytically study friction and dissipation of a driven bead in a 1D harmonic chain, and analyze the role of internal damping mechanism as well as chain length. Specifically, we investigate Dissipative Particle Dynamics and Langevin Dynamics, as paradigmatic examples that do and do not display translational symmetry, with distinct results: For identical parameters, the friction forces can differ by many orders of magnitude. For slow driving, a Goldstone mode traverses the entire system, resulting in friction of the driven bead that grows arbitrarily large (Langevin) or gets arbitrarily small (Dissipative Particle Dynamics) with system size. For a long chain, the friction for DPD is shown to be bound, while it shows a singularity (i.e. can be arbitrarily large) for Langevin damping. For long underdamped chains, a radiation mode is recovered in either case, with friction independent of damping mechanism. For medium length chains, the chain shows the expected resonant behavior. At the resonance, friction is non-analytic in damping parameter γ, depending on it as γ −1. Generally, no zero frequency bulk friction coefficient can be determined, as the limits of small frequency and infinite chain length do not commute, and we discuss the regimes where ‘simple’ macroscopic friction occurs.

Logarithmic soft graviton theorems from superrotation Ward identities

Soft graviton theorems receive one-loop contributions that are logarithmic in the energy of the soft graviton, and which are closely related to tails of gravitational waveforms. We demonstrate that these logarithmic corrections are encoded in the Ward identity of superrotation symmetries, i.e. they follow from conservation of superrotation charge across spatial infinity i0. Our proof relies on a careful analysis of the radiative phase space admitting such gravitational tails, and the determination of the fluxes through null infinity I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{I} $$\\end{document} that act as canonical generators of superrotations on both gravitational and matter fields. All logarithmic terms are derived from the fluxes through correlations of the supertranslation Goldstone mode, provided care is taken in manipulating gravitationally interacting (i.e. dressed) rather than free fields. In cases where massive particles take part in the scattering process, logarithmic corrections also partly arise from the superrotation charge generator at timelike infinity i±.

Universal Features of Entanglement Entropy in the Honeycomb Hubbard Model.

The entanglement entropy is a unique probe to reveal universal features of strongly interacting many-body systems. In two or more dimensions these features are subtle, and detecting them numerically requires extreme precision, a notoriously difficult task. This is especially challenging in models of interacting fermions, where many such universal features have yet to be observed. In this Letter we tackle this challenge by introducing a new method to compute the Rényi entanglement entropy in auxiliary-field quantum MonteCarlo simulations, where we treat the entangling region itself as a stochastic variable. We demonstrate the efficiency of this method by extracting, for the first time, universal subleading logarithmic terms in a two-dimensional model of interacting fermions, focusing on the half-filled honeycomb Hubbard model at T=0. We detect the universal corner contribution due to gapless fermions throughout the Dirac semi-metal phase and at the Gross-Neveu-Yukawa critical point, where the latter shows a pronounced enhancement depending on the type of entangling cut. Finally, we observe the universal Goldstone mode contribution in the antiferromagnetic Mott insulating phase.

Electrons interacting with Goldstone modes and the rotating frame

Electrons interacting with Goldstone modes and the rotating frame

Frame potential of Brownian SYK model of Majorana and Dirac fermions

We consider the Brownian SYK, i.e. a system of N Majorana (Dirac) fermions with a white-noise q-body interaction term. We focus on the dynamics of the Frame potentials, a measure of the scrambling and chaos, given by the moments of the overlap between two independent realisations of the model. By means of a Keldysh path-integral formalism, we compute its early and late-time value. We show that, for q > 2, the late time path integral saddle point correctly reproduces the saturation to the value of the Haar frame potential. On the contrary, for q = 2, the model is quadratic and consistently we observe saturation to the Haar value in the restricted space of Gaussian states (Gaussian Haar). The latter is characterised by larger system size corrections that we correctly capture by counting the Goldstone modes of the Keldysh saddle point. Finally, in the case of Dirac fermions, we highlight and resolve the role of the global U(1) symmetry.

From shockwaves to the gravitational memory effect

We study the relationship between shockwave geometries and the gravitational memory effect in four-dimensional asymptotically flat spacetime. In particular, we show the ’t Hooft commutation relations of shockwave operators are equivalent to the commutation relation between soft and Goldstone modes parametrizing a sector of the gravitational phase space. We demonstrate this equivalence via a diffeomorphism that takes a shockwave metric to a metric whose transverse traceless component is the gravitational memory. The shockwave momentum in ’t Hooft’s analysis is related to the soft graviton mode, which is responsible for the memory effect, while the shift in the shockwave position is related to the Goldstone mode. This equivalence opens new directions to utilize the gravitational memory effect to explore the observational implications of shockwave geometries in flat space.

Time-reversal and parity-time symmetry breaking in non-Hermitian field theories.

We study time-reversal symmetry breaking in non-Hermitian fluctuating field theories with conserved dynamics, comprising the mesoscopic descriptions of a wide range of nonequilibrium phenomena. They exhibit continuous parity-time (PT) symmetry-breaking phase transitions to dynamical phases. For two concrete transition scenarios, exclusive to non-Hermitian dynamics, namely, oscillatory instabilities and critical exceptional points, a low-noise expansion exposes a pretransitional surge of the mesoscale (informatic) entropy production rate, inside the static phases. Its scaling in the susceptibility contrasts conventional critical points (such as second-order phase transitions), where the susceptibility also diverges, but the entropy production generally remains finite. The difference can be attributed to active fluctuations in the wavelengths that become unstable. For critical exceptional points, we identify the coupling of eigenmodes as the entropy-generating mechanism, causing a drastic noise amplification in the Goldstone mode.