Breaking Of Translational Invariance Research Articles

Intrinsic cluster-shaped density waves in cellular dynamical mean-field theory

It is well known that cellular dynamical mean-field theory (CDMFT) leads to the artificial breaking of translation invariance. In spite of this, it is one of the most successful methods to treat strongly correlated electrons systems. Here, we investigate in more detail how this broken translation invariance manifests itself. This allows us to disentangle artificial broken translation invariance effects from the genuine strongly correlated effects captured by CDMFT. We report artificial density waves taking the shape of the cluster---cluster density waves---in all our zero temperature CDMFT solutions, including pair density waves in the superconducting state. We discuss the limitations of periodization regarding this phenomenon, and we present mean-field density-wave models that reproduce CDMFT results at low energy in the superconducting state. We then discuss how these artificial density waves help the agreement of CDMFT with high temperature superconducting cuprates regarding the low-energy spectrum, in particular for subgap structures observed in tunneling microscopy. We relate these subgap structures to nodal and antinodal gaps in our results, similar to those observed in photoemission experiments. This fortuitous agreement suggests that spatial inhomogeneity may be a key ingredient to explain some features of the low-energy underdoped spectrum of cuprates with strongly correlated methods. This work deepens our understanding of CDMFT and clearly identifies signatures of broken translation invariance in the presence of strong correlations.

Chiral soliton lattice in QCD-like theories

Recently, it has been shown that the ground state of quantum chromodynamics (QCD) in sufficiently strong magnetic fields and at moderate baryon number chemical po- tential carries a crystalline condensate of neutral pions: the chiral soliton lattice (CSL) [1]. While the result was obtained in a model-independent manner using effective field the- ory techniques, its realization from first principles using lattice Monte Carlo simulation is hampered by the infamous sign problem. Here we show that CSL, or a similar inhomoge- neous phase, also appears in the phase diagram of a class of vector-like gauge theories that do not suffer from the sign problem even in the presence of a baryon chemical potential and external magnetic field. We also show that the onset of nonuniform order manifests itself already in the adjacent homogeneous Bose-Einstein-condensation phase through a characteristic roton-like minimum in the dispersion relation of the lowest-lying quasipar- ticle mode. Last but not least, our work gives a class of explicit counterexamples to the long-standing conjecture that positivity of the determinant of the Dirac operator (that is, absence of the sign problem) in a vector-like gauge theory precludes spontaneous breaking of translational invariance, and thus implies the absence of inhomogeneous phases in the phase diagram of the theory.

Odd-frequency superconductivity induced by nonmagnetic impurities

A growing body of literature suggests that odd-frequency superconducting pair amplitudes can be generated in normal metal-superconductor junctions. The emergence of odd-frequency pairing in these systems is often attributed to the breaking of translation invariance. In this work, we study the pair symmetry of a one-dimensional $s$-wave superconductor in the presence of a single non-magnetic impurity and demonstrate that translation symmetry breaking is not sufficient for inducing odd-frequency pairing. We consider three kinds of impurities: a local perturbation of the chemical potential, an impurity possessing a quantum energy level, and a local perturbation of the superconducting gap. Surprisingly, we find local perturbations of the chemical potential do not induce any odd-frequency pairing, despite the fact that they break translation invariance. Moreover, although odd-frequency can be induced by both the quantum impurity and the perturbation of the gap, we find these odd-frequency amplitudes emerge from entirely different kinds of scattering processes. The quantum impurity generates odd-frequency pairs by allowing one of the quasiparticles belonging to an equal-time Cooper pair to tunnel onto the impurity state and then back to the superconductor, giving rise to odd-frequency amplitudes with a temporal broadening inversely proportional to the energy level of the impurity. In contrast to this, the perturbation of the gap leads to odd-frequency pairing by "gluing-together" normal state quasiparticles from different points in space and time, leading to odd-frequency amplitudes which are very localized in the time domain.

Surface Ordering in Molecular Clusters by Interactions of Well-Defined Parity Multipoles.

The spontaneous alignment of dipoles in patterns tangential or transversal to the interface of molecular clusters is studied by molecular dynamics simulations throughout the entire aggregation process. Tangential ordering (TANGO) is found to rely on dispersion forces driven by dipolar fluctuations. Transversal ordering (TRANSO) results from the interplay of two conditions: the broken translational invariance at the cluster interface and the interactions of multipoles of opposite parity. In this case, the orientational order parameter at the interface follows a universal scaling law behavior. In the limiting case of strongly interacting particles, a sharp structural transition from a disordered into an ordered state is observed at a critical distance inside the cluster and at a critical magnitude of the dipole moment.

Zoology of solid & fluid holography \u2014 Goldstone modes and phase relaxation

We provide a comprehensive classification of isotropic solid and fluid holographic models with broken translational invariance. We describe in detail the collective modes in both the transverse and longitudinal sectors. First, we discuss holographic fluid models, i.e. systems invariant under internal volume preserving diffeomorphisms. We consider the explicit (EXB) and the spontaneous (SSB) breaking of translations and we emphasize the differences with respect to their solid counterpart. Then, we present a study of the longitudinal collective modes in simple holographic solid and fluid models exhibiting the interplay between SSB and EXB. We confirm the presence of light pseudo-phonons obeying the Gell-Mann-Oakes-Renner relation and the validity of the relation proposed in the literature between the novel phase relaxation scale, the mass of the pseudo-Golstone modes and the Goldstone diffusion. Moreover, we find very good agreement between the dispersion relation of our longitudinal sound mode and the formulae derived from the Hydro+ framework. Finally, our results suggest that the crystal diffusion mode does not acquire a simple damping term because of the novel relaxation scale proportional to the EXB. The dynamics is more complex and it involves the interplay of three modes: the crystal diffusion and two more arising from the splitting of the original sound mode. In this sense, the novel relaxation scale, which comes from the explicit breaking of the global internal shift symmetry of the Stückelberg fields, is different from the one induced by elastic defects, and depending solely on the SSB scale.

Longitudinal sound and diffusion in holographic massive gravity

We consider a simple class of holographic massive gravity models for which the dual field theories break translational invariance spontaneously. We study, in detail, the longitudinal sector of the quasi-normal modes at zero charge density. We identify three hydrodynamic modes in this sector: a pair of sound modes and one diffusion mode. We numerically compute the dispersion relations of the hydrodynamic modes. The obtained speed and the attenuation of the sound modes are in agreement with the hydrodynamic predictions. On the contrary, we surprisingly find disagreement in the case of the diffusive mode; its diffusion constant extracted from the quasi-normal mode data does not agree with the expectations from hydrodynamics. We confirm our numerical results using ana- lytic tools in the decoupling limit and we comment on some possible reasons behind the disagreement. Finally, we extend the analysis of the collective longitudinal modes beyond the hydrodynamic limit by displaying the dynamics of the higher quasi-normal modes at large frequencies and momenta.

Supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas.

Supersolids are exotic materials combining the frictionless flow of a superfluid with the crystal-like periodic density modulation of a solid. The supersolid phase of matter was predicted 50 years ago1-3 for solid helium4-8. Ultracold quantum gases have recently been made to exhibit periodic order typical of a crystal, owing to various types of controllable interaction9-13. A crucial feature of a D-dimensional supersolid is the occurrence of D+1 gapless excitations, reflecting the Goldstone modes associated with the spontaneous breaking of two continuous symmetries: the breaking of phase invariance, corresponding to the locking of the phase of the atomic wave functions at the origin of superfluid phenomena, and the breaking of translational invariance due to the lattice structure of the system. Such modes have been the object of intense theoretical investigations1,14-18, but they have not yet been observed experimentally. Here we demonstrate supersolid symmetry breaking through the appearance of two distinct compressional oscillation modes in a harmonically trapped dipolar Bose-Einstein condensate, reflecting the gapless Goldstone excitations of the homogeneous system. We observe that the higher-frequency mode is associated with an oscillation of the periodicity of the emergent lattice and the lower-frequency mode characterizes the superfluid oscillations. This work also suggests the presence of two separate quantum phase transitions between the superfluid, supersolid and solid-like configurations.

Spectral weight suppression and Fermi arc-like features with strong holographic lattices

We investigate holographic fermions in uni-directional striped phases, where the breaking of translational invariance can be generated either spontaneously or explicitly. We solve the Dirac equation for a probe fermion in the associated background geometry. When the spatial modulation effect becomes sufficiently strong, we see a spectral weight suppression whenever the Fermi surface is larger than the first Brillouin zone. This leads to the gradual disappearance of the Fermi surface along the symmetry breaking direction, in all of the cases we have examined. This effect appears to be a generic consequence of strong inhomogeneities, independently of whether translational invariance is broken spontaneously or explicitly. The resulting Fermi surface is segmented and has features reminiscent of Fermi arcs.

Anomaly-Induced Inhomogeneous Phase in Quark Matter without the Sign Problem

We demonstrate the existence of an anomaly-induced inhomogeneous phase in a class of vectorlike gauge theories without the sign problem, thus disproving the long-standing conjecture that the absence of the sign problem precludes spontaneous breaking of translational invariance. The presence of the phase in the two-color modification of quantum chromodynamics can be tested by an independent nonperturbative evaluation of the neutral pion decay constant as a function of an external magnetic field. Our results provide a benchmark for future lattice studies of inhomogeneous phases in dense quark matter.

Translationally Invariant Universal Classical Hamiltonians

Spin models are widely studied in the natural sciences, from investigating magnetic materials in condensed matter physics to studying neural networks. Previous work has demonstrated that there exist simple classical spin models that are universal: they can replicate—in a precise and rigorous sense—the complete physics of any other classical spin model, to any desired accuracy. However, all previously known universal models break translational invariance. In this paper we show that there exist translationally invariant universal models. Our main result is an explicit construction of a translationally invariant, 2D, nearest-neighbour, universal classical Hamiltonian with a single free parameter. The proof draws on techniques from theoretical computer science, in particular recent complexity theoretic results on tiling problems. Our results imply that there exists a single Hamiltonian which encompasses all classical spin physics, just by tuning a single parameter and varying the size of the lattice. We also prove that our construction is optimal in terms of the number of parameters in the Hamiltonian; there cannot exist a translationally invariant universal Hamiltonian with only the lattice size as a parameter.

The \u03d54 model with the BPS preserving defect

The ϕ4 model is coupled to an impurity in a way that preserves one-half of the BPS property. This means that the antikink-impurity bound state is still a BPS solution, i.e., a zero-pressure solution saturating the topological energy bound. The kink-impurity bound state, on the other hand, does not saturate the bound, in general.We found that, although the impurity breaks translational invariance, it is, in some sense, restored in the BPS sector where the energy of the antikink-impurity solution does not depend on their mutual distance. This is reflected in the existence of a generalised translational symmetry and a zero mode.We also investigate scattering processes. In particular, we compare the antikink-impurity interaction close to the BPS regime, which presents a rather smooth, elastic like nature, with other scattering processes. However, even in this case, after exciting a sufficiently large linear mode on the incoming antikink, we can depart from the close-to-BPS regime. This results, for example, in a backward scattering.

Spontaneous momentum dissipation and coexistence of phases in holographic Horndeski theory

We discuss the possible phases dual to the AdS hairy black holes in Horndeski theory. In the probe limit breaking the translational invariance, we study the conductivity and we find a non-trivial structure indicating a collective excitation of the charge carriers as a competing effect of momentum dissipation and the coupling of the scalar field to Einstein tensor. Going beyond the probe limit, we investigate the spontaneous breaking of translational invariance near the critical temperature and discuss the stability of the theory. We consider the backreaction of the charged scalar field to the metric and we construct numerically the hairy black hole solution. To determine the dual phases of a hairy black hole, we compute the conductivity. When the wave number of the scalar field is zero, the DC conductivity is divergent due to the conservation of translational invariance. For nonzero wave parameter with finite DC conductivity, we find two phases in the dual theory. For low temperatures and for positive couplings, as the temperature is lower, the DC conductivity increases therefore the dual theory is in metal phase, while if the coupling is negative we have the opposite behavior and it is dual to an insulating phase. We argue that this behavior of the coupling of the scalar field to Einstein tensor can be attributed to its role as an impurity parameter in the dual theory.

Universality of the reversal transition in growth phenomena of molecular crystals

ABSTRACTThe fundamental origin of the reversal transition during crystal growth has been investigated by Monte Carlo simulations. Evidence is provided supporting the geometrical nature of the transition, arising from the broken translational invariance at the growth front and the interactions of multipoles of opposed parity. The range of interactions, the details of the force field and model are irrelevant to the occurrence and only determine the functional behaviour of the relevant physical quantities like the localisation of the critical point and the morphology of the phase diagram.

Interaction-induced photon blockade using an atomically thin mirror embedded in a microcavity

Narrow dark resonances associated with electromagnetically induced transparency play a key role in enhancing photon-photon interactions. The schemes realized to date relied on the existence of long-lived atomic states with strong van der Waals interactions. Here, we show that by placing an atomically thin semiconductor with ultra-fast radiative decay rate inside a \textcolor{black}{0D} cavity, it is possible to obtain narrow dark or bright resonances in transmission whose width could be much smaller than that of the cavity and bare exciton decay rates. While breaking of translational invariance places a limit on the width of the dark resonance width, it is possible to obtain a narrow bright resonance that is resilient against disorder by tuning the cavity away from the excitonic transition. Resonant excitation of this bright resonance yields strong photon antibunching even in the limit where the interaction strength is arbitrarily smaller than the non-Markovian disorder broadening and the radiative decay rate of the bare exciton. Our findings suggest that atomically thin semiconductors could pave the way for realization of strongly interacting photonic systems in the solid-state.

Complete homotopy invariants for translation invariant symmetric quantum walks on a chain

We provide a classification of translation invariant one-dimensional quantum walks with respect to continuous deformations preserving unitarity, locality, translation invariance, a gap condition, and some symmetry of the tenfold way. The classification largely matches the one recently obtained (arXiv:1611.04439) for a similar setting leaving out translation invariance. However, the translation invariant case has some finer distinctions, because some walks may be connected only by breaking translation invariance along the way, retaining only invariance by an even number of sites. Similarly, if walks are considered equivalent when they differ only by adding a trivial walk, i.e., one that allows no jumps between cells, then the classification collapses also to the general one. The indices of the general classification can be computed in practice only for walks closely related to some translation invariant ones. We prove a completed collection of simple formulas in terms of winding numbers of band structures covering all symmetry types. Furthermore, we determine the strength of the locality conditions, and show that the continuity of the band structure, which is a minimal requirement for topological classifications in terms of winding numbers to make sense, implies the compactness of the commutator of the walk with a half-space projection, a condition which was also the basis of the general theory. In order to apply the theory to the joining of large but finite bulk pieces, one needs to determine the asymptotic behaviour of a stationary Schrödinger equation. We show exponential behaviour, and give a practical method for computing the decay constants.

Axionic black branes with conformal coupling

We find neutral and charged black brane solutions with axion fields in the context of a conformally coupled gravitational theory in four dimensions. These solutions describe anti--de Sitter (AdS) black branes supported by axion fields that break translational invariance at the boundary, which provides momentum dissipation. The conformally coupled scalar field is regular inside and outside the event horizon and there is no need for any self-interaction, obtaining in this way solutions without fine-tuned parameters. We analyze the thermodynamics of our solutions considering the effects of the axionic charges. In asymptotically AdS configurations, the axionic and electric charges are related, implying vanishing scalar field contributions to the mass. The rotating solution is obtained by means of a Lorentz boost having angular momentum sustained by the axion parameter. We compute the holographic DC conductivity and we show how it is affected by the inclusion of the conformal scalar field, which provides a temperature-independent behavior. Finally, we include a $k$-essence term that modifies the DC conductivity and provides more general behaviors.

Holography and thermalization in optical pump-probe spectroscopy

Using holography, we model experiments in which a 2+1D strange metal is pumped by a laser pulse into a highly excited state, after which the time evolution of the optical conductivity is probed. We consider a finite-density state with mildly broken translation invariance and excite it by oscillating electric field pulses. At zero density, the optical conductivity would assume its thermalized value immediately after the pumping has ended. At finite density, pulses with significant DC components give rise to slow exponential relaxation, governed by a vector quasinormal mode. In contrast, for high-frequency pulses the amplitude of the quasinormal mode is strongly suppressed, so that the optical conductivity assumes its thermalized value effectively instantaneously. This surprising prediction may provide a stimulus for taking up the challenge to realize these experiments in the laboratory. Such experiments would test a crucial open question faced by applied holography: Are its predictions artefacts of the large $N$ limit or do they enjoy sufficient UV independence to hold at least qualitatively in real-world systems?

Boomerang RG flows with intermediate conformal invariance

For a class of D = 5 holographic models we construct boomerang RG flow solutions that start in the UV at an AdS5 vacuum and end up at the same vacuum in the IR. The RG flows are driven by deformations by relevant operators that explicitly break translation invariance. For specific models, such that they admit another AdS5 solution, AdS5c, we show that for large enough deformations the RG flows approach an intermediate scaling regime with approximate conformal invariance governed by AdS5c. For these flows we calculate the holographic entanglement entropy and the entropic c-function for the RG flows. The latter is not monotonic, but it does encapsulate the degrees of freedom in each scaling region. For a different set of models, we find boomerang RG flows with intermediate scaling governed by an AdS2 × ℝ3 solution which breaks translation invariance. Furthermore, for large enough deformations these models have interesting and novel thermal insulating ground states for which the entropy vanishes as the temperature goes to zero, but not as a power-law. Remarkably, the thermal diffusivity and the butterfly velocity for these new insulating ground states are related via D = EvB2/(2πT), with E(T) → 0.5 as T → 0.

Holographic model for the anomalous scalings of the cuprates

We examine transport in a holographic model in which the dynamics of the charged degrees of freedom is described by the nonlinear Dirac-Born-Infeld (DBI) action. Axionic scalar fields are included to break translational invariance and generate momentum dissipation in the system. Scaling exponents are introduced by using geometries which are nonrelativistic and hyperscaling-violating in the infrared. In the probe DBI limit the theory reproduces the anomalous temperature dependence of the resistivity and Hall angle of the cuprate strange metals, $\rho \sim T$ and $\cot\Theta_H \sim T^2$. These scaling laws would not be present without the nonlinear dynamics encoded by the DBI interactions. We further show that because of its richness the DBI theory supports a wide spectrum of temperature scalings. This model provides explicit examples in which transport is controlled by different relaxation times. On the other hand, when only one quantity sets the temperature scale of the system, the Hall angle and conductivity typically exhibit the same temperature behavior. We illustrate this point using new fully backreacted analytical dyonic black brane solutions.

Flavours and infra-red instability in holography

With a simple gravitational model in five dimensions, defined by Einstein-gravity with a negative cosmological constant, coupled to a Dirac-Born-Infeld and a Chern-Simons term, we explore the fate of BF-bound violation for a probe scalar field and a fluctuation mode of the corresponding geometry. We assume this simple model to capture the dynamics of a strongly coupled SU(Nc) gauge theory with Nf fundamental matter, which in the limit mathcal{O}left({N}_cright)sim mathcal{O}left({N}_fright) and with a non-vanishing matter density, is holographically described by an AdS2-geometry in the IR. We demonstrate that, superconductor/superfluid instabilities are facilitated and spontaneous breaking of translational invariance is inhibited with increasing values of (Nf/Nc). This is similar, in spirit, with known results in large Nc Quantum Chromodynamics with Nf quarks and a non-vanishing density, in which the chiral density wave phase becomes suppressed and superconducting instabilities become favoured as the number of quarks is increased.