Spontaneous Breaking Of Translational Invariance Research Articles

On the hydrodynamics of (2 + 1)-dimensional strongly coupled relativistic theories in an external magnetic field

In this paper, we review recent progress on relativistic hydrodynamics in (2 + 1) dimensions with an external magnetic field. We discuss the formalism allowing for momentum loss due to the explicit and spontaneous breaking of translation invariance by scalar operators. We also compare to some results from the gauge/gravity correspondence.

Higher-order topological quantum paramagnets

Quantum paramagnets are strongly-correlated phases of matter where competing interactions frustrate magnetic order down to zero temperature. In certain cases, quantum fluctuations induce instead topological order, supporting, in particular, fractionalized quasi-particle excitations. In this work, we investigate paradigmatic spin models and show how magnetic frustration can also give rise to higher-order topological properties. We first study the frustrated Heisenberg model in a square lattice, where a plaquette valence bond solid appears through the spontaneous breaking of translational invariance. Despite the amount of effort that has been devoted to study this phase, its topological nature has so far been overlooked. By means of tensor network simulations, we establish how such state belongs to a higher-order symmetry-protected topological phase, where long-range plaquette order and non-trivial topology coexist. This interplay allows the system to support excitations that would be absent otherwise, such as corner-like states in the bulk attached to dynamical topological defects. Finally, we demonstrate how this higher-order topological quantum paramagnet can also be induced by dipolar interactions, indicating the possibility to directly observe this phase using atomic quantum simulators.

On the universality of AdS2 diffusion bounds and the breakdown of linearized hydrodynamics

The chase of universal bounds on diffusivities in strongly coupled systems and holographic models has a long track record. The identification of a universal velocity scale, independent of the presence of well-defined quasiparticle excitations, is one of the major challenges of this program. A recent analysis, valid for emergent IR fixed points exhibiting local quantum criticality, and dual to IR AdS2 geometries, suggests to identify such a velocity using the time and length scales at which hydrodynamics breaks down — the equilibration velocity. The latter relates to the radius of convergence of the hydrodynamic expansion and it is extracted from a collision between a hydrodynamic diffusive mode and a non-hydrodynamic mode associated to the IR AdS2 region. In this short note, we confirm this picture for holographic systems displaying the spontaneous breaking of translational invariance. Moreover, we find that, at zero temperature, the lower bound set by quantum chaos and the upper one defined by causality and hydrodynamics exactly coincide, determining uniquely the diffusion constant. Finally, we comment on the meaning and universality of this newly proposed prescription.

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.

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.

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.

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.

Towards a holographic quark matter crystal

We construct the gravity dual of d = 4, mathcal{N}=4 , SU(Nc) super Yang-Mills theory, coupled to Nf flavors of dynamical quarks, at non-zero temperature T and nonzero quark density Nq. The supergravity solutions possess a regular horizon if T > 0 and include the backreaction of Nc color D3-branes and Nf flavor D7-branes with Nq units of electric flux on their worldvolume. At zero temperature the solutions interpolate between a Landau pole singularity in the ultraviolet and a Lifshitz geometry in the infrared. At high temperature the thermodynamics is directly sensitive to the Landau pole, whereas at low temperature it is not, as expected from effective field theory. At low temperature and sufficiently high charge density we find thermodynamic and dynamic instabilities towards the spontaneous breaking of translation invariance.

Strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux

We perform a density-matrix renormalization-group study of strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux. Focusing on one-third filling, we explore the phase diagram in dependence of the magnetic flux and the inter-leg tunneling strength. We find several phases including a Meissner phase, vortex liquids, a vortex lattice, as well as a staggered-current (SC) phase. Moreover, there are regions where the chiral current reverses its direction, both in the Meissner and in the SC phase. While the reversal in the latter case can be ascribed to spontaneous breaking of translational invariance, in the first it stems from an effective flux increase in the rung direction. Interactions are a necessary ingredient to realize either type of chiral-current reversal.

Holographic Stripes

We construct inhomogeneous asymptotically AdS black hole solutions corresponding to the spontaneous breaking of translational invariance and the formation of striped order in the boundary field theory. We find that the system undergoes a second order phase transition in both the fixed density and fixed chemical potential ensembles, for sufficiently large values of the axion coupling. We investigate the phase structure as function of the temperature, axion coupling and the stripe width. The bulk solutions have striking geometrical features related to a magnetoelectric effect associated with the existence of a near horizon topological insulator. At low temperatures the horizon becomes highly inhomogeneous and tends to pinch off.}

Abrikosov-Nielsen-Olesen string with non-Abelian moduli and spin-orbit interactions.

It is generally believed that the spontaneous breaking of the Poincaré group by flux tubes (strings) generates only two zero modes localized on the string and associated with the spontaneous breaking of translational invariance (the so-called Low-Manohar argument). Being perfectly true in many instances this argument is nevertheless nonuniversal and has to be amended in the case of order parameters carrying spatial indices. We show that under certain circumstances additional zero (or quasizero) modes can appear due to spin symmetry.

Modulated ground state of gravity theories with stabilized conformal factor

We discuss the stabilization of the conformal factor by higher derivative terms in a conformally reduced $R+R^2$ Euclidean gravity theory. The flat spacetime is unstable towards the condensation of modes with nonzero momentum, and they "condense" in a modulated phase above a critical value of the coupling $\beta$ of the $R^2$ term. By employing a combination of variational, numerical and lattice methods we show that in the semiclassical limit the corresponding functional integral is dominated by a single nonlinear plane wave of frequency $\approx 1/\sqrt{\beta} \lp$. We argue that the ground state of the theory is characterized by a spontaneous breaking of translational invariance at Planckian scales.

Spontaneous breaking of translational invariance in noncommutativeλϕ4theory in two dimensions

The spontaneous breaking of translational invariance in noncommutative self-interacting scalar field theory in two dimensions is investigated by effective action techniques. The analysis confirms the existence of the stripe phase, already observed in lattice simulations, due to the nonlocal nature of the noncommutative dynamics.

Rigidity of crystalline color superconducting quark matter

We calculate the shear modulus of crystalline color superconducting quark matter, showing that this phase of dense, but not asymptotically dense, three-flavor quark matter responds to shear stress like a very rigid solid. To evaluate the shear modulus, we derive the low-energy effective Lagrangian that describes the phonons that originate from the spontaneous breaking of translation invariance by the spatial modulation of the gap parameter $\ensuremath{\Delta}$. These massless bosons describe space- and time-dependent fluctuations of the crystal structure and are analogous to the phonons in ordinary crystals. The coefficients of the spatial derivative terms of the phonon effective Lagrangian are related to the elastic moduli of the crystal; the coefficients that encode the linear response of the crystal to a shearing stress define the shear modulus. We analyze the two particular crystal structures which are energetically favored over a wide range of densities, in each case evaluating the phonon effective action and the shear modulus up to order ${\ensuremath{\Delta}}^{2}$ in a Ginzburg-Landau expansion, finding shear moduli which are 20 to 1000 times larger than those of neutron star crusts. The crystalline color superconducting phase has long been known to be a superfluid---by picking a phase its order parameter breaks the quark-number $U(1{)}_{B}$ symmetry spontaneously. Our results demonstrate that this superfluid phase of matter is at the same time a rigid solid. We close with a rough estimate of the pinning force on the rotational vortices which would be formed embedded within this rigid superfluid upon rotation. Our results raise the possibility that (some) pulsar glitches could originate within a quark matter core deep within a neutron star.

Induced gravity and universe creation on the domain wall in five-dimensional space-time

We present a model with a strong fermion self-interaction and an induced gravitational interaction in five-dimensional space-time. In the strong-coupling regime, this model develops a spontaneous breaking of translational invariance, which results in localizing light particles on the (3+1)-dimensional domain wall embedded in the anti-de Sitter five-dimensional space-time. We obtain the corresponding low-energy effective action and investigate kink-type vacuum solutions in a quasiflat Riemannian metric. We discuss the physics of light particles in 3+1 dimensions and establish the fundamental relations between the induced gravitational constant and both the curvature in the five-dimensional anti-de Sitter space-time and the Newton gravitational constant of our universe.

KK-masses in dipole deformed field theories

We reconsider aspects of non-commutative dipole deformations of field theories. Among our findings there are hints to new phases with spontaneous breaking of translation invariance (stripe phases), similar to what happens in Moyal-deformed field theories. Furthermore, using zeta-function regularization, we calculate quantum corrections to KK-state masses. The corrections coming from non-planar diagrams show interesting but non-universal behaviour. Depending on the type of interaction the corrections can make the KK-states very heavy but also very light or even tachyonic. Finally we point out that the dipole deformation of QED is not renormalizable!

Spontaneous breaking of translational invariance in one-dimensional stationary states on a ring

We consider a model in which positive and negative particles diffuse in an asymmetric, CP-invariant way on a ring. The positive particles hop clockwise, the negative counterclockwise and oppositely-charged adjacent particles may swap positions. Monte-Carlo simulations and analytic calculations suggest that the model has three phases; a "pure" phase in which one has three pinned blocks of only positive, negative particles and vacancies, and in which translational invariance is spontaneously broken, a "mixed" phase with a non-vanishing current in which the three blocks are positive, negative and neutral, and a disordered phase without blocks.

Stability conditions and the single mode approximation in FQHE

A thermodynamic stability criterion for the spontaneous breaking of translation invariance in many particle systems is derived. It simply requires the positive character of the wavevector dependent dielectric function, generalishing the same condition for macroscopic dielectric constants. Its application to the single mode approximation (SMA) for the description of collective modes of the v = 1 m Laughlin states is considered. The results indicate that the stability condition is violated by the SMA for all the relevant states m = 3, 5, 7, 9 in a wavevector neighborhood of the magneto-roton minima. These conclusions are in qualitative agreement with similar results obtained from the solution of the Bethe-Salpeter equation at v = 1 3 for both composite fermions and phenomenologically described electrons in the Laughlin state.

Nonlinear theory of modulated standing waves; domain walls, kinks and breathers

A nonlinear theory of modulated standing waves is developed in one dimension. The existence of various localized solutions is elucidated. These include: domain walls , which characterize the transition between regions of different wave number, kinks , which describe a shift in the phase of the oscillation, and lower cut-off breathers . All of these states correspond to a spontaneous breaking of translational invariance, while the domain wall in addition represents a broken parity. Except for the breathers, the modulational equations that describe these states take a form that differs from the sine-Gordon, nonlinear Schrödinger, Toda lattice and Korteweg de Vries equations. In addition to the hamiltonian limit, the case of damped parametrically driven motion is also discussed.

Microscopic theory for cross-linked macromolecules. I. Broken symmetry, rigidity, and topology.

This paper is concerned with the onset of rigidity in randomly cross-linked macromolecules. We discuss in detail the possible partitionings of configuration space, which may accompany the spontaneous breaking of translational invariance, treating separately the cases of crystals, amorphous solids, and cross-linked macromolecules. We describe the order parameters for these systems, drawing the distinction between solids with discrete translational symmetry and solids with macroscopic translational invariance, such as randomly cross-linked macromolecular solids. We show that the latter may be described by a sequence of probability distributions for the overlaps of equilibrium states. In a cross-linked system of impenetrable linear chains, the configuration space of the solid state is partitioned into two categories of equilibrium states: those related by translational and rotational symmetry, and those unrelated by these symmetries. The latter are a consequence of the distinct topologies of the network, which are consistent with a given set of cross links. We show how the overlap-probability distributions may be calculated.