Quantum Melting Research Articles

Fractonic gauge theory of smectics

Motivated by striped correlated quantum matter, and the recently developed duality between elasticity of a two-dimensional (2D) crystal and a gauge theory, we derive a dual coupled U(1) vector gauge theory for a two-dimensional (2D) quantum smectic, where the disclination is mapped onto the fractonic charge, that we demonstrate can only move transversely to smectic layers. This smectic gauge theory dual also emerges from a gauge dual of a quantum crystal through a Higgs transition corresponding to a single flavor of its dipole condensation, an anisotropic quantum melting via dislocation proliferation. A condensation of the second flavor of dislocations a corresponds to another Higgs transition describing the smectic-to-nematic melting. We also utilize the electrostatic limit of this duality to formulate a melting of a 2D classical smectic in terms of a higher derivative sine–Gordon model, demonstrating its instability to a nematic at any nonzero temperature. Generalizing this classical duality to a 3D smectic, gives formulation of a 3D nematic-to-smectic transition in terms of an anisotropic Abelian-Higgs model.

Quantum Smectic Gauge Theory.

We present a gauge theory formulation of a two-dimensional quantum smectic and its relatives, motivated by their realizations in correlated quantum matter. The description gives a unified treatment of phonons and topological defects, respectively, encoded in a pair of coupled gauge fields and corresponding charges. The charges exhibit subdimensional constrained quantum dynamics and anomalously slow highly anisotropic diffusion of disclinations inside a smectic. This approach gives a transparent description of a multistage quantum melting transition of a two-dimensional commensurate crystal (through an incommensurate crystal-a supersolid) into a quantum smectic, which subsequently melts into a quantum nematic and isotropic superfluids, all in terms of a sequence of Higgs transitions.

Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting

Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase.

Phase behavior of the quantum Lennard-Jones solid.

The Lennard-Jones (LJ) potential is perhaps one of the most widely used models for the interaction of uncharged particles, such as noble gas solids. The phase diagram of the classical LJ solid is known to exhibit transitions between hcp and fcc phases. However, the phase behavior of the quantum LJ solid remains unknown. Thermodynamic integration based on path integral molecular dynamics (PIMD) and lattice dynamics calculations are used to study the phase stability of the hcp and fcc LJ solids. The hcp phase is shown to be stabilized by quantum effects in PIMD, while fcc is shown to be favored by lattice dynamics, which suggests a possible re-entrant low pressure fcc phase for highly quantum systems. Implications for the phase stability of noble gas solids are discussed. For parameters equating to helium, the expansion due to zero-point vibrations is associated with quantum melting: neither crystal structure is stable at zero pressure.

Thermal and Quantum Melting Phase Diagrams for a Magnetic-Field-Induced Wigner Solid.

A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting two-dimensional (2D) system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array in order to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at low temperatures and very small Landau level filling factors (ν≃1/5). In dilute GaAs 2D hole systems, on the other hand, thanks to the larger hole effective mass and the ensuing Landau level mixing, the WS forms at relatively higher fillings (ν≃1/3). Here we report our measurements of the fundamental temperature vs filling phase diagram for the 2D holes' WS-liquid thermal melting. Moreover, via changing the 2D hole density, we also probe their Landau level mixing vs filling WS-liquid quantum melting phase diagram. We find our data to be in good agreement with the results of very recent calculations, although intriguing subtleties remain.

Theory of collective magnetophonon resonance and melting of a field-induced Wigner solid

Electron solid phases of matter are revealed by characteristic vibrational resonances. Sufficiently large magnetic fields can overcome the effects of disorder, leading to a weakly pinned collective mode called the magnetophonon. Consequently, in this regime it is possible to develop a tightly constrained hydrodynamic theory of pinned magnetophonons. The behavior of the magnetophonon resonance across thermal and quantum melting transitions has been experimentally characterized in two-dimensional electron systems. Applying our theory to these transitions we explain several key features of the data: (i) violation of the Fukuyama-Lee sum rule as the transition is approached is directly tied to the non-Lorentzian form taken by the resonance and (ii) the non-Lorentzian shape is caused by characteristic dissipative channels that become especially important close to melting: proliferating dislocations and uncondensed charge carriers.

Symmetry-enforced fractonicity and two-dimensional quantum crystal melting

Fractons are particles that cannot move in one or more directions without paying energy proportional to their displacement. Here, we introduce the concept of symmetry enforced fractonicity, in which particles are fractons in the presence of a global symmetry, but are free to move in its absence. A simple example is dislocation defects in a two-dimensional crystal, which are restricted to move only along their Burgers vector due to particle number conservation. Utilizing a recently developed dual rank-2 tensor gauge description of elasticity, we show that accounting for their symmetry enforced one-dimensional nature of dislocation motion dramatically alters the structure of quantum crystal melting phase transitions. We show that, at zero temperature, sufficiently strong quantum fluctuations of the crystal lattice favor the formation of a super-solid phase that spontaneously breaks the symmetry enforcing fractonicity of defects. The defects can then condense to drive the crystal into a super-nematic phase via a phase transition in the $2+1d$ XY universality class to drive a melting phase transition of the crystal to a nematic phase. This scenario contrasts the standard Halperin-Nelson scenario for thermal melting of $2d$ solids in which dislocations can proliferate via a single continuous thermal phase transition. We comment on the application of these results to other scenarios such as vortex lattice melting at a magnetic field induced superconductor-insulator transition, and quantum melting of charge density waves of stripes in a metal.

Charged and neutral fixed points in the O(N)⊕O(N) model with Abelian gauge fields

In the Abelian-Higgs model, or Ginzburg-Landau model of superconductivity, the existence of an infrared stable charged fixed point ensures that there is a parameter range where the superconducting phase transition is second order, as opposed to fluctuation-induced first order as one would infer from the Coleman-Weinberg mechanism. We study the charged and neutral fixed points of a two-field generalization of the Abelian-Higgs model, where two N-component fields are coupled to two gauge fields and to each other, using the functional renormalization group. Focusing mostly on three dimensions, in the neutral case, this is a model for two-component Bose-Einstein condensation, and we confirm the fixed-point structure established in earlier works using different methods. The charged model is a dual theory of two-dimensional dislocation-mediated quantum melting. We find the existence of three charged fixed points for all N>2, while there are additional fixed points for N=2.

Strange metal from a frustration-driven charge order instability.

Interparticle interactions are self-conflicting rather than cooperative on particular lattices. When such geometrical frustration occurs, charge ordering (CO) can be destabilized into non-trivial charge states such as the recently observed charge glass (CG). A more extreme case is the frustration-induced quantum melting of the CO that has been theoretically proposed. Here, we report d.c. charge transport and noise spectroscopy measurements for a triangular-lattice organic conductor situated close to the CO or CG. Our experiments demonstrate that these materials can host a strange metal with unusual charge dynamics, which we attribute to frustration-induced fluctuations of the CO or CG. Our results also show that the anomalous charge fluctuations can freeze into an insulating state when uniaxial stress is applied, which reduces the geometrical frustration. The present observations suggest the existence of the frustration-induced quantum melting of charges analogous to spin liquids.

Dynamical structure factor of the triangular antiferromagnet: Schwinger boson theory beyond mean field

We compute the zero temperature dynamical structure factor $S({\bf q},\omega)$ of the triangular lattice Heisenberg model (TLHM) using a Schwinger boson approach that includes the Gaussian fluctuations ($1/N$ corrections) of the saddle point solution. While the ground state of this model exhibits a well-known 120$^{\circ}$ magnetic ordering, experimental observations have revealed a strong quantum character of the excitation spectrum. We conjecture that this phenomenon arises from the proximity of the ground state of the TLHM to the quantum melting point separating the magnetically ordered and spin liquid states. Within this scenario, magnons are described as collective modes (two spinon-bound states) of a spinon condensate (Higgs phase) that spontaneously breaks the SU(2) symmetry of the TLHM. Crucial to our results is the proper account of this spontaneous symmetry breaking. The main qualitative difference relative to semi-classical treatments ($1/S$ expansion) is the presence of a high-energy spinon continuum extending up to about three times the single-magnon bandwidth. In addition, the magnitude of the ordered moment ($m=0.224$) agrees very well with numerical results and the low energy part of the single-magnon dispersion is in very good agreement with series expansions. Our results indicate that the Schwinger boson approach is an adequate starting point for describing the excitation spectrum of some magnetically ordered compounds that are near the quantum melting point separating this Higgs phase from the {\it deconfined} spin liquid state.

Dual gauge field theory of quantum liquid crystals in three dimensions

The dislocation-mediated quantum melting of solids into quantum liquid crystals is extended from two to three spatial dimensions, using a generalization of boson-vortex or Abelian-Higgs duality. Dislocations are now Burgers-vector-valued strings that trace out worldsheets in spacetime while the phonons of the solid dualize into two-form (Kalb-Ramond) gauge fields. We propose an effective dual Higgs potential that allows for restoring translational symmetry in either one, two or three directions, leading to the quantum analogues of columnar, smectic or nematic liquid crystals. In these phases, transverse phonons turn into gapped, propagating modes while compressional stress remains massless. Rotational Goldstone modes emerge whenever translational symmetry is restored. We also consider electrically charged matter, and find amongst others that as a hard principle only two out of the possible three rotational Goldstone modes are observable using electromagnetic means.

Emergence of chiral spin liquids via quantum melting of noncoplanar magnetic orders

Quantum spin liquids (QSLs) are long-range entangled states of quantum magnets which lie beyond the Landau paradigm of classifying phases of matter via broken symmetries. A physical route to arriving at QSLs is via frustration-induced quantum melting of ordered states such as valence bond crystals or magnetic orders. Here, we show, using extensive exact diagonalization (ED) and density-matrix renormalization group (DMRG) studies of concrete $SU(2)$ invariant spin models on honeycomb, triangular and square lattices, that chiral spin liquids (CSLs) emerge as descendants of triple-$Q$ spin crystals with tetrahedral magnetic order and a large scalar spin chirality. Such ordered-to-CSL melting transitions may yield lattice realizations of effective Chern-Simons-Higgs field theories. Our work provides a distinct unifying perspective on the emergence of CSLs, and suggests that materials with magnetic skyrmion crystal order might provide a good starting point to search for CSLs.

Quantum Melting and Isotope Effects from Diffusion Monte Carlo Studies of p-H2 Clusters.

We present a rigorous characterization of the ground state structures of p-H2 clusters and their isotopologues using diffusion Monte Carlo combined with the inherent structures analysis. For the N = 19 cluster we explore the effect of "quantum melting" by quantifying the contributions of local minima to the ground state as a function of continuously varying particle mass. Doubling the cluster size leads to an enormous increase of its complexity: the ground state of (p-H2)38 is highly delocalized over a large number of minima representing all the funnels of the potential energy surface. The ground state of (o-D2)38 is also delocalized, but over a smaller subset of minima, which exclusively belong to the same disordered motif.

Quantum and thermal melting of stripe forming systems with competing long-range interactions

We study the quantum melting of stripe phases in models with competing short range and long range interactions decaying with distance as $1/r^{\sigma}$ in two space dimensions. At zero temperature we find a two step disordering of the stripe phases with the growth of quantum fluctuations. A quantum critical point separating a phase with long range positional order from a phase with long range orientational order is found when $\sigma \leq 4/3$, which includes the Coulomb interaction case $\sigma=1$. For $\sigma > 4/3$ the transition is first order, which includes the dipolar case $\sigma=3$. Another quantum critical point separates the orientationally ordered (nematic) phase from a quantum disordered phase for any value of $\sigma$. Critical exponents as a function of $\sigma$ are computed at one loop order in an $\epsilon$ expansion and, whenever available, compared with known results. For finite temperatures it is found that for $\sigma \geq 2$ orientational order decays algebraically with distance until a critical Kosterlitz-Thouless line. Nevertheless, for $\sigma < 2$ it is found that long range orientational order can exist at finite temperatures until a critical line which terminates at the quantum critical point at $T=0$. The temperature dependence of the critical line near the quantum critical point is determined as a function of $\sigma$.

Vortex patterns in moderately rotating Bose-condensed gas

Using exact diagonalization, we investigate the many-body ground state for regular vortex patterns in a rotating Bose-condensed gas of N spinless particles, confined in a quasi-two-dimensional harmonic trap and interacting repulsively via finite-range Gaussian potential. The N-body Hamiltonian matrix is diagonalized in given subspaces of quantized total angular momentum Lz, to obtain the lowest-energy eigenstate. Further, the internal structure of these eigenstates is analyzed by calculating the corresponding conditional probability distribution. Specifically, the quantum mechanically stable as well as unstable states in a co-rotating frame are examined in the moderately rotating regime corresponding to angular momenta for N = 16 bosons. In response to externally impressed rotation, the patterns of singly quantized vortices are formed, shaping into canonical polygons with a central vortex at the trap center. The internal structure of unstable states reveals the mechanism of entry, nucleation and pattern formation of vortices with structural phase transition, as the condensate goes from one stable vortical state to the other. The stable polygonal vortex patterns having discrete p-fold rotational symmetry with p = 5 and p = 6 are observed. The hexagonal vortex pattern with p = 6 symmetry is a precursor to the triangular vortex lattice of singly quantized vortices in the thermodynamic limit. For unstable states, quantum melting of vortex patterns due to uncertainty in positions of individual vortices, is also briefly discussed.

Double vibronic process in the quantum spin ice candidate Tb2Ti2O7 revealed by terahertz spectroscopy

The origin of quantum fluctuations responsible for the spin liquid state in Tb$_2$Ti$_2$O$_7$ has remained a long standing problem. By synchrotron-based terahertz measurements, we show evidence of strong coupling between the magnetic and lattice degrees of freedom that provides a path to the quantum melting process. As revealed by hybrid crystal electric field-phonon excitations that appear at 0.67 THz below 200 K, and around 0.42 THz below 50 K, the double vibronic process is unique for Tb$^{3+}$ in the titanate family due to adequate energy matching and strong quadrupolar moments. The results suggest that lattice motion can indeed be the driving force behind spin flips within the hybridized ground and first excited states, promoting quantum terms in the effective Hamiltonian that describes Tb$_2$Ti$_2$O$_7$.

Quantum melting of two-component Rydberg crystals

We investigate the quantum melting of one dimensional crystals that are realized in an atomic lattice in which ground state atoms are laser excited to two Rydberg states. We focus on a regime where both, intra- and inter-state density-density interactions as well as coherent exchange interactions contribute. We determine stable crystalline phases in the classical limit and explore their melting under quantum fluctuations introduced by the excitation laser as well as two-body exchange. We find that within a specific parameter range quantum fluctuations introduced by the laser can give rise to a devil's staircase structure which one might associate with transitions in the classical limit. The melting through exchange interactions is shown to also proceed in a step-like fashion, in case of small crystals, due to the proliferation of Rydberg spinwaves.

The Helium Field Effect Transistor (II): Gated Transport of Surface-State Electrons Through Micro-constrictions

We present transport measurements of surface-state electrons on liquid helium films in confined geometry. The measurements are taken using split-gate devices similar to a field effect transistor. The number of electrons passing between the source and drain areas of the device can be precisely controlled by changing the length of the voltage pulse applied to the gate electrode. We find evidence that the effective driving potential depends on electron–electron interactions, as well as the electric field applied to the substrate. Our measurements indicate that the mobility of electrons on helium films can be high and that microfabricated transistor devices allow electron manipulation on length scales close to the interelectron separation. Our experiment is an important step toward investigations of surface-state electron properties at much higher densities, for which the quantum melting of the system to a degenerate Fermi gas should be observed.

Quantum melting of magnetic order in an organic dimer Mott-insulating system

Quantum entanglement effects between the electronic spin and charge degrees of freedom are examined in an organic molecular solid, termed a dimer-Mott insulating system, in which molecular dimers are arranged in a crystal as fundamental units. A low energy effective model includes an antisymmetric exchange interaction, as one of the dominant magnetic interactions. This interaction favors a 90 degree spin configuration, and competes with the Heisenberg-type exchange interaction. Stabilities of the magnetic ordered phases are examined by using the spin-wave theory, as well as the Schwinger-boson theory. It is found that the spin-charge interaction promotes an instability of the long-range magnetic ordered state around a parameter region where two spin-spiral phases are merged. Implication for the quantum spin liquid state observed in $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ is discussed.

Role of confinements on the melting of Wigner molecules in quantum dots

We analyze the quantum melting of two-dimensional Wigner molecules (WM) in confined geometries with distinct symmetries and compare it with corresponding thermal melting. Our findings unfold complementary mechanisms that drive the quantum and thermal crossovers in a WM and show that the symmetry of the confinement plays no significant role in determining the quantum crossover scale $n_X$. This is because the zero-point motion screens the boundary effects within short distances. The phase diagram as a function of thermal and quantum fluctuations determined from independent criteria is unique, and shows "melting" from the WM to both the classical and quantum "liquids." An intriguing signature of weakening liquidity with increasing temperature, $T$, is found in the extreme quantum regime. The crossover is associated with production of defects. However, these defects appear to play distinct roles in driving the quantum and thermal "melting." Our study will help comprehending melting in a variety of experimental traps - from quantum dots to complex plasma.