Spontaneous Breaking Of Translational Symmetry Research Articles

A holographic perspective on phonons and pseudo-phonons

We analyze the concomitant spontaneous breaking of translation and conformal symmetries by introducing in a CFT a complex scalar operator that acquires a spatially dependent expectation value. The model, inspired by the holographic Q-lattice, provides a privileged setup to study the emergence of phonons from a spontaneous translational symmetry breaking in a conformal field theory and offers valuable hints for the treatment of phonons in QFT at large. We first analyze the Ward identity structure by means of standard QFT techniques, considering both spontaneous and explicit symmetry breaking. Next, by implementing holographic renormalization, we show that the same set of Ward identities holds in the holographic Q-lattice. Eventually, relying on the holographic and QFT results, we study the correlators realizing the symmetry breaking pattern and how they encode information about the low-energy spectrum.

Speed limit in internal space of domain walls via all-order effective action of moduli motion

We find that motion in internal moduli spaces of generic domain walls has an upper bound for its velocity. Our finding is based on our generic formula for all-order effective actions of internal moduli parameter of domain wall solitons. It is known that the Nambu-Goldstone mode $Z$ associated with spontaneous breaking of translation symmetry obeys a Nambu-Goto effective Lagrangian $\sqrt{1 - (\partial_0 Z)^2}$ detecting the speed of light ($|\partial_0 Z|=1$) in the target spacetime. Solitons can have internal moduli parameters as well, associated with a breaking of internal symmetries such as a phase rotation acting on a field. We obtain, for generic domain walls, an effective Lagrangian of the internal moduli $\epsilon$ to all order in $(\partial \epsilon)$. The Lagrangian is given by a function of the Nambu-Goto Lagrangian: $L = g(\sqrt{1 + (\partial_\mu \epsilon)^2})$. This shows generically the existence of an upper bound on $\partial_0 \epsilon$, i.e. a speed limit in the internal space. The speed limit exists even for solitons in some non-relativistic field theories, where we find that $\epsilon$ is a type I Nambu-Goldstone mode which also obeys a nonlinear dispersion to reach the speed limit. This offers a possibility of detecting the speed limit in condensed matter experiments.

Observing the Rosensweig instability of a quantum ferrofluid.

Ferrofluids exhibit unusual hydrodynamic effects owing to the magnetic nature of their constituents. As magnetization increases, a classical ferrofluid undergoes a Rosensweig instability and creates self-organized, ordered surface structures or droplet crystals. Quantum ferrofluids such as Bose-Einstein condensates with strong dipolar interactions also display superfluidity. The field of dipolar quantum gases is motivated by the search for new phases of matter that break continuous symmetries. The simultaneous breaking of continuous symmetries such as the phase invariance in a superfluid state and the translational symmetry in a crystal provides the basis for these new states of matter. However, interaction-induced crystallization in a superfluid has not yet been observed. Here we use in situ imaging to directly observe the spontaneous transition from an unstructured superfluid to an ordered arrangement of droplets in an atomic dysprosium Bose-Einstein condensate. By using a Feshbach resonance to control the interparticle interactions, we induce a finite-wavelength instability and observe discrete droplets in a triangular structure, the number of which grows as the number of atoms increases. We find that these structured states are surprisingly long-lived and observe hysteretic behaviour, which is typical for a crystallization process and in close analogy to the Rosensweig instability. Our system exhibits both superfluidity and, as we show here, spontaneous translational symmetry breaking. Although our observations do not probe superfluidity in the structured states, if the droplets establish a common phase via weak links, then our system is a very good candidate for a supersolid ground state.

Holographic lattices and metal–insulator transition

This paper is an extension of the talk given at the conference on Gravitation and Cosmology/The Fourth Galileo-Xu Guangqi Meeting. We intend to present a short review on recent progress on the construction of holographic lattices and its application to metal–insulator transition (MIT), which is a fundamentally important phenomenon in condensed matter physics. We will firstly implement the Peierls phase transition by constructing holographic charge density waves which are induced by the spontaneous breaking of translational symmetry. Then we turn to the holographic realization of metal–insulator transition as a quantum critical phenomenon with many strongly correlated electrons involved. The holographic entanglement entropy as a diagnostic for such quantum phase transitions will be briefly mentioned.

Scalar fields in a non-commutative space

We discuss the λϕ4 model in 2- and 3-dimensional non-commutative spaces. The mapping onto a Hermitian matrix model enables its non-perturbative investigation by Monte Carlo simulations. The numerical results reveal a phase where stripe patterns dominate. In d = 3 we show that in this phase the dispersion relation is deformed in the IR regime, in agreement with the property of UV/IR mixing. This “striped phase” also occurs in d = 2. For both dimensions we provide evidence that it persists in the simultaneous limit to the continuum and to infinite volume (“Double Scaling Limit”). This implies the spontaneous breaking of translation symmetry.

Spin- and Pair-Density-Wave Glasses

Spontaneous breaking of translational symmetry---known as `density wave' order---is common in nature. However such states are strongly sensitive to impurities or other forms of frozen disorder leading to fascinating glassy phenomena. We analyze impurity effects on a particularly ubiquitous form of broken translation symmetry in solids: a Spin Density Wave (SDW) with spatially modulated magnetic order. Related phenomena occur in Pair Density Wave (PDW) superconductors where the superconducting order is spatially modulated. For weak disorder, we find that the SDW / PDW order can generically give way to a SDW / PDW glass---new phases of matter with a number of striking properties, which we introduce and characterize here. In particular, they exhibit an interesting combination of conventional (symmetry-breaking) and spin glass (Edwards-Anderson) order. This is reflected in the dynamic response of such a system, which---as expected for a glass---is extremely slow in certain variables, but---surprisingly---is fast in others. Our results apply to all uniaxial metallic SDW systems where the ordering vector is incommensurate with the crystalline lattice. In addition, the possibility of a PDW glass has important consequences for some recent theoretical and experimental work on $La_{2-x}Ba_xCu_2O_4$.

Integer versus Fractional Charge Transfer at Metal(/Insulator)/Organic Interfaces: Cu(/NaCl)/TCNE.

Semilocal and hybrid density functional theory was used to study the charge transfer and the energy-level alignment at a representative interface between an extended metal substrate and an organic adsorbate layer. Upon suppressing electronic coupling between the adsorbate and the substrate by inserting thin, insulating layers of NaCl, the hybrid functional localizes charge. The laterally inhomogeneous charge distribution resulting from this spontaneous breaking of translational symmetry is reflected in observables such as the molecular geometry, the valence and core density of states, and the evolution of the work function with molecular coverage, which we discuss for different growth modes. We found that the amount of charge transfer is determined, to a significant extent, by the ratio of the lateral spacing of the molecules and their distance to the metal. Therefore, charge transfer does not only depend on the electronic structure of the individual components but, just as importantly, on the interface geometry.

The continuum phase diagram of the 2d non-commutative λϕ 4 model

We present a non-perturbative study of the lambda phi**4 model on a non-commutative plane. The lattice regularised form can be mapped onto a Hermitian matrix model, which enables Monte Carlo simulations. Numerical data reveal the phase diagram; at large lambda it contains a "striped phase", which is absent in the commutative case. We explore the question whether or not this phenomenon persists in a Double Scaling Limit (DSL), which extrapolates simultaneously to the continuum and to infinite volume, at a fixed non-commutativity parameter. To this end, we introduce a dimensional lattice spacing based on the decay of the correlation function. Our results provide evidence for the existence of a striped phase even in the DSL, which implies the spontaneous breaking of translation symmetry. Due to the non-locality of this model, this does not contradict the Mermin-Wagner Theorem.

Collective excitations of a laser driven atomic condensate in an optical cavity

We theoretically examine collective excitations of an optically driven atomic Bose–Einstein condensate, coupled to a high-finesse optical cavity. This open system has been recently used for the experimental demonstration of the Dicke superradiance of cavity photons, which is simultaneously and mutually triggered by spontaneous breaking of translational symmetry of the condensate into a crystalline order. We first develop a Hartree–Fock mean field dynamical model of the physical system. Using this model, we compute the dynamics of the cavity photons, the condensate density profile and the Dicke phase transition diagram. Both the imaginary-time and real-time evolution methods are used in the calculations. Collective excitations are determined by the solving Bogoliubov–de Gennes equations. The spectrum, softening of the modes and energetic hierarchy of excitations are determined.

Spontaneous Pattern Formation in an Antiferromagnetic Quantum Gas

In this Letter we report on the spontaneous formation of surprisingly regular periodic magnetic patterns in an antiferromagnetic Bose-Einstein condensate (BEC). The structures evolve within a quasi-one-dimensional BEC of 87Rb atoms on length scales of a millimeter with typical periodicities of 20…30 μm, given by the spin healing length. We observe two sets of characteristic patterns which can be controlled by an external magnetic field. We identify these patterns as linearly unstable modes within a mean-field approach and calculate their mode structure as well as time and energy scales, which we find to be in good agreement with observations. These investigations open new prospects for controlled studies of symmetry breaking and complex quantum magnetism in bulk BEC.

Tuning the Shape of the Condensate in Spontaneous Symmetry Breaking

We investigate the conditions which determine the shape of a particle condensate in situations when it emerges as a result of spontaneous breaking of translational symmetry. We consider a model with particles hopping between sites of a one-dimensional grid and interacting if they are at the same site or at neighboring sites. We predict the envelope of the condensate and the scaling of its width with the system size for various interaction potentials and show how to tune the shape from a delta peak to a rectangular or paraboliclike form.

Standard model of fermions on the domain wall in five-dimensional space-time

The mechanism of generation of the Standard Model for fermions on the domain wall in five-dimensional space-time is presented. As a result of self-interaction of five-dimensional fermions and gravity induced by matter fields, in the strong coupling regime, in the model there arises a spontaneous translational symmetry breaking, which leads to localization of light particles on a 3 + 1-dimensional domain wall (“3-brane”) that is embedded into a five-dimensional anti-de Sitter space-time (AdS5). Appropriate low-energy, effective action, classical kink-like vacuum configurations for the gravity and scalar fields are investigated. Mass spectra for light composite particles and their coupling constants interaction in ultra-low-energy, which localize on the brane, are explored. We establish estimates of characteristic scales and constants interactions of the model and also a relation between the bulk five-dimensional gravitational constant, curvature of AdS5 space-time, and brane Newton’s constants. The induced cosmological constant on the brane exactly vanishes in all orders of the theory perturbation. We find out that scalar interaction is strongly suppressed at ultra-low-energy, and the brane fluctuations (branons) are suitable “sterile” canditates for explanation of the phenomenon of Dark Matter. Bibliography: 21 titles.

Self-localization of holes in a lightly doped Mott insulator

We show that lightly doped holes will be self-trapped in an antiferromagnetic spin background at low-temperatures, resulting in a spontaneous translational symmetry breaking. The underlying Mott physics is responsible for such novel self-localization of charge carriers. Interesting transport and dielectric properties are found as the consequences, including large doping-dependent thermopower and dielectric constant, low-temperature variable-range-hopping resistivity, as well as high-temperature strange-metal-like resistivity, which are consistent with experimental measurements in the high-T$_c$ cuprates. Disorder and impurities only play a minor and assistant role here.

On nonhomogeneous Bose condensation

We prove, in great generality, that in a system of bosons, whenever Bose condensation in a nonzero mode occurs then there is also spontaneous breaking of translation symmetry. In particular the proof holds for realistic Bose systems with two-body superstable interaction. This generalizes an old result proving that the occurrence of Bose-Einstein condensation in the zero mode implies spontaneous breaking of gauge invariance.

Brane world generation by matter and gravity

We present a non-compact (4 + 1) dimensional model with a local strong four-fermion interaction supplementing it with gravity. In the strong coupling regime it reveals the spontaneous translational symmetry breaking which eventually leads to the formation of domain walls, or thick 3-branes, embedded in the AdS-5 manifold. To describe this phenomenon we construct the appropriate low-energy effective Action and find kink-like vacuum solutions in the quasi-flat Riemannian metric. We discuss the generation of ultra-low-energy (3 + 1) dimensional physics and we establish the relation among the bulk five dimensional gravitational constant, the brane Newton's constants and the curvature of AdS-5 space-time. The plausible relation between the compositeness scale of the scalar matter and the symmetry breaking scale is shown to support the essential decoupling of branons, the scalar fluctuations of the brane, from the Standard Model matter, supporting their possible role in the dark matter saturation. The induced cosmological constant on the brane does vanish due to exact cancellation of matter and gravity contributions.

Magnetization plateaus in frustrated antiferromagnetic quantum spin models

Plateaus can be observed in the zero-temperature magnetization curve of quantum spinsystems at rational values of the magnetization. In one dimension, the appearance of aplateau is controlled by a quantization condition for the magnetization which involves thelength of the local spin and the volume of a translational unit cell of the ground state. Wediscuss examples of geometrically frustrated quantum spin systems with large (in generalunbounded) periodicities of spontaneous breaking of translational symmetry in the groundstate.In two dimensions, we discuss the square, triangular and Kagomé lattices using exact diagonalization (ED) forup to N = 40 sites.For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at onethird of the saturation magnetization. The Kagomé lattice gives rise to particularly richbehaviour with several plateaus in the magnetization curve and a jump due to localmagnon excitations just below saturation.

Orbital dimerization inNaTiSi2O6:An orbital analogue of the spin-Peierls phase transition

We measure the Raman scattering spectra of ${\mathrm{NaTiSi}}_{2}{\mathrm{O}}_{6},$ analyze the vibrational properties, and study the origin of the phase transition in this compound. In this quasi-one-dimensional $S=1/2$ system we observe anomalous high-temperature phonon broadenings, and large changes of the phonon energies and line-widths across the phase transition temperature of 210 K. These results, combined with theoretical considerations, indicate that the phonon anomalies originate from an orbital order-disorder type of phase transition. We find that the high temperature dynamical Jahn-Teller phase of ${\mathrm{NaTiSi}}_{2}{\mathrm{O}}_{6}$ exhibits a spontaneous breaking of translational symmetry into a dimerized, Jahn-Teller distorted, orbital ordered state under the formation of spin valence bonds.

Orbital dimerization in NaTiSi2O6. An orbital analogue of the spin-Peierls phase transition

Abstract The phonon dynamics in NaTiSi2O6 is studied using the Raman scattering technique. The observed phonon anomalies around T=210 K combined with theoretical considerations show that the high-temperature dynamical Jahn–Teller phase of NaTiSi2O6 exhibits a spontaneous breaking of translational symmetry into an orbital dimerized state. We describe this phase instability as an orbital analogue of the spin-Peierls phase transition.

Non‐commutative field theories beyond perturbation theory

AbstractWe investigate two models in non‐commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally reduced matrix models. Using this technique, we measure Wilson loops in 2d NC gauge theory of rank 1. It turns out that they are non‐perturbatively renormalizable, and the phase follows an Aharonov‐Bohm effect if we identify θ = 1/B. Next we study the 3d λ ϕ4 model with two NC coordinates, where we present new results for the correlators and the dispersion relation. We further reveal the explicit phase diagram. The ordered regime splits into a uniform and a striped phase, as it was qualitatively conjectured before. We also confirm the recent observation by Ambjø rn and Catterall that such stripes occur even in d = 2, although they imply the spontaneous breaking of translation symmetry. However, in d = 3 and d = 2 we observe only patterns of two stripes to be stable in the range of parameters investigated.