Spontaneous Breaking Of Translational Symmetry Research Articles

Anomalous Hall Crystals in Rhombohedral Multilayer Graphene. I. Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field.

Recent experiments on rhombohedral pentalayer graphene with a substrate-induced moiré potential have identified both Chern insulators and fractional quantum Hall states at zero magnetic field. Surprisingly, these states are observed in strong displacement fields where the effects of the moiré lattice are weak, and seem to be readily accessed without fine-tuning. To address these experimental puzzles, we study a model of interacting electrons in this geometry. Within self-consistent Hartree-Fock (SCHF) calculations, we find an isolated Chern band with small bandwidth and good quantum geometry. Exact diagonalization and density-matrix renormalization group calculations both confirm the band hosts fractional quantum Hall states without a magnetic field. Remarkably, the Chern band is stable at a wide range of angles, at four through six rhombohedral layers, at varying rhombohedral hopping parameters, and-most strikingly-survives in SCHF calculations when the moiré potential vanishes. In this limit, the state spontaneously breaks time-reversal and translation symmetry simultaneously, giving a topological crystalline state that we term the "anomalous Hall crystal." We argue this is a general mechanism to create stable Chern bands in rhombohedral multilayer graphene, opening the door to studying the interplay between electronic topology, fractionalization, and spontaneous translation symmetry breaking.

Between waves and patterns: Spin wave freezing in films with Dzyaloshinskii-Moriya interaction

The relationship between waves and static pattern formation is an intriguing effect and remains unexplained in many areas of physics, including magnetism. We study the spin-wave-mediated spin reorientation transition (SRT) in magnetic films with uniaxial magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI). In particular, we show that propagating spin waves can freeze in the SRT, causing periodic magnetic domains to arise, which is reminiscent of the wave amplitude distribution. This process can take place under the influence of a change in the magnetic field, but also of other parameters. Interestingly, at the SRT, DMI nonreciprocity leads to the emergence of flowing magnetization patterns, which suggests a spontaneous breaking of translational symmetry, and the formation of magnonic space-time crystals. The described phenomena are general and should take place in a large family of magnetic materials. Therefore, the results should be of great importance for the further development of spintronics and magnonics.

Ground-state phase diagram of the extended two-leg t−J ladder

Inspired by the observation of a robust $d$-wave superconducting phase driven by tuning the next-nearest-neighbor (NNN) electron hopping in recent density matrix renormalization group (DMRG) studies of six- and eight-leg $t$-$J$ model, we systematically study the phase diagram of the two-leg $t$-$J$ ladder with the NNN couplings (including NNN hopping and spin interaction) in a large region of doping level, by means of the DMRG calculations. Upon doping from half filling, we identify the Luther-Emery liquid (LEL) phase, which can be distinguished as the pairing-dominant and charge density-dominant regime by comparing the Luttinger parameter $K_{\rho}$. With the growing NNN couplings, pairing correlations are enhanced and correspondingly $K_{\rho}$ increases, driving the system from the density-dominant to the pairing-dominant regime. In the Tomonaga-Luttinger liquid (TLL) phase in the larger doping region, we identify two TLL regimes with different features of charge density correlation. At the quarter filling ($1/2$ doping level), we find that the strong dimer orders of bond energy in the open system actually decay algebraically and thus do not indicate a spontaneous translational symmetry breaking. Our results show that in the LEL phase of the two-leg ladder, the NNN couplings seem to play the similar role as that on the wider $t$-$J$ cylinder, and studies on this more accessible system can be helpful towards understanding the emergence of the remarkable $d$-wave superconducting phase on the wider system.

Optical nonlinearities and spontaneous translational symmetry breaking in driven-dissipative moiré exciton-polaritons

Moir\'e lattices formed from semiconductor bilayers host tightly localized excitons that can simultaneously couple strongly to light and possess large electric dipole moments. This facilitates the realization of new forms of polaritons that are very strongly interacting and that have been predicted to lead to strong optical nonlinearities controlled by multiphoton resonances. Here we investigate the role of the nonlocal component of the exciton-exciton (dipolar) interactions on the optical response of these strongly interacting moir\'e exciton-polaritons under conditions of strong optical driving. We find that the nonlocal interactions can strongly influence the steady-state properties leading to multistabilities with spontaneously broken translational symmetry and pronounced distortions of the multiphoton resonances. We develop a self-consistent approach to describe the steady-state solution of moir\'e excitons coupled to a cavity field, treating the long-range interaction between the excitons and the photon field at the semiclassical level.

Superconducting spin smecticity evidencing the Fulde-Ferrell-Larkin-Ovchinnikov state in Sr2RuO4.

Translational symmetry breaking is antagonistic to static fluidity but can be realized in superconductors, which host a quantum-mechanical coherent fluid formed by electron pairs. A peculiar example of such a state is the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, induced by a time-reversal symmetry-breaking magnetic field applied to spin-singlet superconductors. This state is intrinsically accompanied by the superconducting spin smecticity, spin density-modulated fluidity with spontaneous translational-symmetry breaking. Detection of such spin smecticity provides unambiguous evidence for the FFLO state, but its observation has been challenging. Here, we report the characteristic "double-horn" nuclear magnetic resonance spectrum in the layered superconductor Sr2RuO4 near its upper critical field, indicating the spatial sinusoidal modulation of spin density that is consistent with superconducting spin smecticity. Our work reveals that Sr2RuO4 provides a versatile platform for studying FFLO physics.

Revisiting Anderson-Higgs mechanism: application of Lieb-Schultz-Mattis theorem

We consider an electron model of superconductivity on a three-dimensional lattice where there are on-site attractive Hubbard interaction and long-range repulsive Coulomb interaction. It is claimed that fully gapped s-wave superconductivity within this model, if present, exhibits spontaneous translation symmetry breaking possibly related to a charge order. Our discussions are based on an application of the Lieb-Schultz-Mattis theorem under some physical assumptions. The inconsistency between the proposed supersolid and experiments can impose some constraints on a reasonable choice of a theoretical model.

Holographic phonons by gauge-axion coupling

In this paper, we show that a simple generalization of the holographic axion model can realize spontaneous breaking of translational symmetry by considering a special gauge-axion higher derivative term. The finite real part and imaginary part of the stress tensor imply that the dual boundary system is a viscoelastic solid. By calculating quasi-normal modes and making a comparison with predictions from the elasticity theory, we verify the existence of phonons and pseudo-phonons, where the latter is realized by introducing a weak explicit breaking of translational symmetry, in the transverse channel. Finally, we discuss how the phonon dynamics affects the charge transport.

Phase relaxation and pattern formation in holographic gapless charge density waves

We study the dynamics of spontaneous translation symmetry breaking in holographic models in presence of weak explicit sources. We show that, unlike conventional gapped quantum charge density wave systems, this dynamics is well characterized by the effective time dependent Ginzburg-Landau equation, both above and below the critical temperature, which leads to a “gapless” algebraic pattern of metal-insulator phase transition. In this framework we elucidate the nature of the damped Goldstone mode (the phason), which has earlier been identified in the effective hydrodynamic theory of pinned charge density wave and observed in holographic homogeneous lattice models. We follow the motion of the quasinormal modes across the dynamical phase transition in models with either periodic inhomogeneous or helical homogeneous spatial structures, showing that the phase relaxation rate is continuous at the critical temperature. Moreover, we find that the qualitative low-energy dynamics of the broken phase is universal, insensitive to the precise pattern of translation symmetry breaking, and therefore applies to homogeneous models as well.

Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics

Recently, quantum simulation of low-dimensional lattice gauge theories (LGTs) has attracted many interests, which may improve our understanding of strongly correlated quantum many-body systems. Here, we propose an implementation to approximate ℤ2 LGT on superconducting quantum circuits, where the effective theory is a mixture of a LGT and a gauge-broken term. By using matrix product state based methods, both the ground state properties and quench dynamics are systematically investigated. With an increase of the transverse (electric) field, the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase. In the ordered phase, an approximate Gauss law of the ℤ2 LGT emerges in the ground state. Moreover, to shed light on the experiments, we also study the quench dynamics, where there is a dynamical signature of the spontaneous translational symmetry breaking. The spreading of the single particle of matter degree is diffusive under the weak transverse field, while it is ballistic with small velocity for the strong field. Furthermore, due to the emergent Gauss law under the strong transverse field, the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping. Our results pave the way for simulating the LGT on superconducting circuits, including the quantum phase transition and quench dynamics.

Breaking translational symmetry via polymer chain overcrowding in molecular bottlebrush crystallization

One of the fundamental laws in crystallization is translational symmetry, which accounts for the profound shapes observed in natural mineral crystals and snowflakes. Herein, we report on the spontaneous formation of spherical hollow crystals with broken translational symmetry in crystalline molecular bottlebrush (mBB) polymers. The unique structure is named as mBB crystalsome (mBBC), highlighting its similarity to the classical molecular vesicles. Fluorescence resonance energy transfer (FRET) experiments show that the mBBC formation is driven by local chain overcrowding-induced asymmetric lamella bending, which is further confirmed by correlating crystalsome size with crystallization temperature and mBBʼs side chain grafting density. Our study unravels a new principle of spontaneous translational symmetry breaking, providing a general route towards designing versatile nanostructures.

Tensor Network Approach to Phase Transitions of a Non-Abelian Topological Phase.

The non-Abelian topological phase with Fibonacci anyons minimally supports universal quantum computation. In order to investigate the possible phase transitions out of the Fibonacci topological phase, we propose a generic quantum-net wave function with two tuning parameters dual with each other, and the norm of the wave function can be exactly mapped into a partition function of the two-coupled ϕ^{2}-state Potts models, where ϕ=(sqrt[5]+1)/2 is the golden ratio. By developing the tensor network representation of this wave function on a square lattice, we can accurately calculate the full phase diagram with the numerical methods of tensor networks. More importantly, it is found that the non-Abelian Fibonacci topological phase is enclosed by three distinct nontopological phases and their dual phases of a single ϕ^{2}-state Potts model: the gapped dilute net phase, critical dense net phase, and spontaneous translation symmetry breaking gapped phase. We also determine the critical properties of the phase transitions among the Fibonacci topological phase and those nontopological phases.

Structural transition in the collective behavior of cognitive agents

Living organisms process information to interact and adapt to their surroundings with the goal of finding food, mating, or averting hazards. The structure of their environment has profound repercussions through both selecting their internal architecture and also inducing adaptive responses to environmental cues and stimuli. Adaptive collective behavior underpinned by specialized optimization strategies is ubiquitous in the natural world. We develop a minimal model of agents that explore their environment by means of sampling trajectories. The spatial information stored in the sampling trajectories is our minimal definition of a cognitive map. We find that, as cognitive agents build and update their internal, cognitive representation of the causal structure of their environment, complex patterns emerge in the system, where the onset of pattern formation relates to the spatial overlap of cognitive maps. Exchange of information among the agents leads to an order-disorder transition. As a result of the spontaneous breaking of translational symmetry, a Goldstone mode emerges, which points at a collective mechanism of information transfer among cognitive organisms. These findings may be generally applicable to the design of decentralized, artificial-intelligence swarm systems.

Discrete time quasicrystals

Between space crystals and amorphous materials there exists a third class of aperiodic structures which lack translational symmetry but reveal long-range order. They are dubbed quasi-crystals and their formation, similarly as the formation of space crystals, is related to spontaneous breaking of translational symmetry of underlying Hamiltonians. Here, we investigate spontaneous emergence of quasi-crystals in periodically driven systems. We consider a quantum many-body system which is driven by a harmonically oscillating force and show that interactions between particles result in spontaneous self-reorganization of the motion of a quantum many-body system and in the formation of a quasi-crystal structure in time.

A simple holographic model for spontaneous breaking of translational symmetry

It has been shown that holographic massive gravities can effectively realize spontaneous breaking of translational symmetry in homogenous manners. In this work, we consider a toy model of such category by adding a special gauge-axion coupling to the bulk action. Firstly, we identify the existence of spontaneous breaking of translations by the analysis on the UV expansion. In the absence of explicit breaking, the black hole solution is simply the same as the Reissner-Nodström(RN) black holes, regardless of the non-trivial profile of the bulk axions. The associated Goldstone modes exist only when the charge density is non-zero. Then, we investigate the optical conductivity both analytically as well as numercially. Our result perfectly agrees with that for a clean system, while the incoherent conductivity gets modified due to the symmetry breaking. The transverse Goldstone modes are dispersionless since the solution is dual to a liquid state. Finally, the effect of momentum relaxation to the transverse modes is considered. In this case, the would-be massless modes are pinned at certain frequency, which is another key difference from the unbroken states.

Temporally, spatially, or lightlike modulated vacua in Lorentz invariant theories

We study the vacuum structure of a class of Lorentz invariant field theories where the vacuum expectation values are not constant but are (phase) modulated. The vacua are classified into spatial, temporal, and light-like modulation types according to the patterns of spontaneous breaking of translational symmetry. The conditions for having temporal or light-like modulated vacua imply severe constraints on the models. We utilize the notion of generalized Nambu-Goldstone modes which appear in the modulated vacua. Finally, we examine fluctuation modes around these vacua and discuss their dynamics and the absence of ghosts.

Intrinsic translational symmetry breaking in a doped Mott insulator

Whether a doped hole propagates as a Bloch wave or not is an important issue of doped Mott physics. Here we examine this problem based on the quasiparticle spectral weight $Z$ distribution, calculated by density matrix renormalization group (DMRG). By tuning the anisotropy of a two-leg $t$-$J$ ladder without closing the background spin gap, the $Z$ distribution unambiguously reveals a transition of the single hole state from a Bloch wave to a novel one with spontaneous translational symmetry breaking. We further establish a direct connection of such a transition with a nonlocal phase string entanglement between the hole and quantum spins, which explains numerical observations.

Scale invariance with fundamental matters and anomaly: a holographic description

Generally, quantum field theories can be thought as deformations away from conformal field theories. In this article, with a simple bottom up model assumed to possess a holographic description, we study a putative large N quantum field theory with large and arbitrary number of adjoint and fundamental degrees of freedom and a non-vanishing chiral anomaly, in the presence of an external magnetic field and with a non-vanishing density. Motivated by the richness of quantum chromodynamics under similar condition, we explore the solution space to find an infinite class of scale-invariant, but not conformal, field theories that may play a pivotal role in defining the corresponding physics. In particular, we find two classes of geometries: Schrödinger isometric and warped AdS3 geometries with an SL(2, R)×U(1) isometry. We find hints of spontaneous breaking of translational symmetry, at low temperatures, around the warped backgrounds.

Generalized global symmetries in states with dynamical defects: The case of the transverse sound in field theory and holography

In this work, we show how states with conserved numbers of dynamical defects (strings, domain walls, etc.) can be understood as possessing generalised global symmetries even when the microscopic origins of these symmetries are unknown. Using this philosophy, we build an effective theory of a $2+1$-dimensional fluid state with two perpendicular sets of immersed elastic line defects. When the number of defects is independently conserved in each set, then the state possesses two one-form symmetries. Normally, such viscoelastic states are described as fluids coupled to Goldstone bosons associated with spontaneous breaking of translational symmetry caused by the underlying microscopic structure---the principle feature of which is a transverse sound mode. At the linear, non-dissipative level, we verify that our theory, based entirely on symmetry principles, is equivalent to a viscoelastic theory. We then build a simple holographic dual of such a state containing dynamical gravity and two two-form gauge fields, and use it to study its hydrodynamic and higher-energy spectral properties characterised by non-hydrodynamic, gapped modes. Based on the holographic analysis of transverse two-point functions, we study consistency between low-energy predictions of the bulk theory and the effective boundary theory. Various new features of the holographic dictionary are explained in theories with higher-form symmetries, such as the mixed-boundary-condition modification of the quasinormal mode prescription that depends on the running coupling of the boundary double-trace deformations. Furthermore, we examine details of low- and high-energy parts of the spectrum that depend on temperature, line defect densities and the renormalisation group scale.

Holographic Phonons.

We present a class of holographic massive gravity models that realize a spontaneous breaking of translational symmetry-they exhibit transverse phonon modes whose speed relates to the elastic shear modulus according to elasticity theory. Massive gravity theories thus emerge as versatile and convenient theories to model generic types of translational symmetry breaking: explicit, spontaneous, and a mixture of both. The nature of the breaking is encoded in the radial dependence of the graviton mass. As an application of the model, we compute the temperature dependence of the shear modulus and find that it features a glasslike melting transition.

Frustrated quantum magnetism in the Kondo lattice on the zigzag ladder

The interplay between Kondo effect, indirect magnetic interaction and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group (DMRG), the ground state and various short- and long-range spin- and density-correlation functions are calculated for the model at half-filling as a function of the antiferromagnetic Kondo interaction down to $J=0.3t$ where $t$ is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-$J$ limit, where almost local Kondo screening dominates and where the system is a nonmagnetic Kondo insulator, antiferromagnetic correlations between nearest-neighbor and next-nearest-neighbor local spins become stronger and stronger, until at $J^{\rm dim}_{\rm c} \approx 0.89t$ frustration is alleviated by a spontaneous breaking of translational symmetry and a corresponding transition to a dimerized state. This is characterized by antiferromagnetic correlations along the legs and by alternating antiferro- and ferromagnetic correlations on the rungs of the ladder. A mechanism of partial Kondo screening that has been suggested for the Kondo lattice on the two-dimensional triangular lattice is not realized in the one-dimensional case. Furthermore, within the symmetry-broken dimerized state, there is a magnetic transition to a $90^{\circ}$ quantum spin spiral with quasi-long-range order at $J^{\rm mag}_{\rm c} \approx 0.84t$. The quantum-critical point is characterized by a closure of the spin gap (with decreasing $J$) and a divergence of the spin-correlation length and of the spin-structure factor $S(q)$ at wave vector $q=\pi/2$. This is opposed to the model on the one-dimensional bipartite chain, which is known to have a finite spin gap for all $J>0$ at half-filling.