Nearest-neighbor Repulsion Research Articles

Exact ground states for pentagon chains with spin–orbit interaction

Exact ground states (GS) are deduced for conducting polymers possessing pentagon type of unit cell. The study is done in the presence of many-body spin–orbit interaction (SOI), local and nearest-neighbor Coulomb repulsion (CR), and presence of external E electric and B magnetic fields (EF). The simultaneous presence of SOI, CR, and EF in the exact conducting polymer GS is a novelty, so the development of the technique for the treatment possibility of such strongly correlated cases is presented in detail. The deduced GS show a broad spectrum of physical characteristics ranging from charge density waves doubling the system periodicity, metal–insulator transitions, to interesting external field-driven effects as, e.g., modification possibility of a static charge distribution by a static EF.Graphic abstract

Frustrated Extended Bose-Hubbard Model and Deconfined Quantum Critical Points with Optical Lattices at the Antimagic Wavelength.

The study of geometrically frustrated many-body quantum systems is of central importance to uncover novel quantum mechanical effects. We design a scheme where ultracold bosons trapped in a one-dimensional state-dependent optical lattice are modeled by a frustrated Bose-Hubbard Hamiltonian. A derivation of the Hamiltonian parameters based on Cesium atoms, further show large tunability of contact and nearest-neighbor interactions. For pure contact repulsion, we discover the presence of two phases peculiar to frustrated quantum magnets: the bond-order-wave insulator with broken inversion symmetry and a chiral superfluid. When the nearest-neighbor repulsion becomes sizable, a further density-wave insulator with broken translational symmetry can appear. We show that the phase transition between the two spontaneously symmetry-broken phases is continuous, thus representing a one-dimensional deconfined quantum critical point not captured by the Landau-Ginzburg-Wilson symmetry-breaking paradigm. Our results provide a solid ground to unveil the novel quantum physics induced by the interplay of nonlocal interactions, geometrical frustration, and quantum fluctuations.

Intertwined Van Hove Singularities as a Mechanism for Loop Current Order in Kagome Metals.

Recent experiments on kagome metals AV_{3}Sb_{5} (A=Cs,Rb,K) indicated spontaneous time-reversal symmetry breaking in the charge density wave state in the absence of static magnetization. The loop current order (LCO) is proposed as its cause, but a microscopic model explaining the emergence of LCO through electronic correlations has not been firmly established. We show that the coupling between van Hove singularities with distinct mirror symmetries is a key ingredient to generate LCO ground state. By constructing an effective model, we find that when multiple van Hove singularities with opposite mirror eigenvalues are close in energy, the nearest-neighbor electron repulsion favors a ground state with coexisting LCO and charge bond order. It is then demonstrated that this mechanism applies to the kagome metals AV_{3}Sb_{5}. Our findings provide an intriguing mechanism of LCO and pave the way for a deeper understanding of complex quantum phenomena in kagome systems.

Phase transitions in the driven lattice gas (TASEP) with repulsive energies

We report on non-equilibrium phase transitions in the driven lattice gas model totally asymmetric exclusion processes caused by nearest-neighbor (NN) repulsions between particles, ɛ > 0, employing extensive Monte Carlo simulations and mean-field calculations. The diagra of phase regimes has five different regimes which are separated by distinct boundaries. We discuss the density of particles and the current which depend differently in the various regimes on the system’s entry and exit rates of particles, α and β, respectively. The steady state can be described by quasi-particles called ‘soft dimerons’, where each dimeron consists of a particle dragging an empty NN site on its left. The asymptotic state of dimerons at is equivalent to the state of hard dimers at ɛ = 0. Since the model is a uni-directional fluid, it has an internal hydrodynamic pressure which increases with increasing inter-particle repulsion ɛ. This leads to a collective effect which causes phase transitions between high and low densities of particles at certain critical points ɛ c .

Superconductivity, Charge Density Wave, and Supersolidity in Flat Bands with a Tunable Quantum Metric.

Predicting the fate of an interacting system in the limit where the electronic bandwidth is quenched is often highly nontrivial. The complex interplay between interactions and quantum fluctuations driven by the band geometry can drive competition between various ground states, such as charge density wave order and superconductivity. In this work, we study an electronic model of topologically trivial flat bands with a continuously tunable Fubini-Study metric in the presence of on-site attraction and nearest-neighbor repulsion, using numerically exact quantum MonteCarlo simulations. By varying the electron filling and the minimal spatial extent of the localized flat-band Wannier wave functions, we obtain a number of intertwined orders. These include a phase with coexisting charge density wave order and superconductivity, i.e., a supersolid. In spite of the nonperturbative nature of the problem, we identify an analytically tractable limit associated with a "small" spatial extent of the Wannier functions and derive a low-energy effective Hamiltonian that can well describe our numerical results. We also provide unambiguous evidence for the violation of any putative lower bound on the zero-temperature superfluid stiffness in geometrically nontrivial flat bands.

Eight-vertex criticality in the interacting Kitaev chain

We show that including pairing and repulsion into the description of 1D spinless fermions, as in the domain wall theory of commensurate melting or the interacting Kitaev chain, leads, for strong enough repulsion, to a line of critical points in the eight vertex universality class terminating floating phases with emergent U(1) symmetry. For nearest-neighbor repulsion and pairing, the variation of the critical exponents along the line that can be extracted from Baxter's exact solution of the XYZ chain at $J_x=-J_z$ is fully confirmed by extensive DMRG simulations of the entire phase diagram, and the qualitative features of the phase diagram are shown to be independent of the precise form of the interactions.

Stationary solutions and local equations for interacting diffusions on regular trees

We study the invariant measures of infinite systems of stochastic differential equations (SDEs) indexed by the vertices of a regular tree. These invariant measures correspond to Gibbs measures associated with certain continuous specifications, and we focus specifically on those measures which are homogeneous Markov random fields. We characterize the joint law at any two adjacent vertices in terms of a new two-dimensional SDE system, called the “local equation”, which exhibits an unusual dependence on a conditional law. Exploiting an alternative characterization in terms of an eigenfunction-type fixed point problem, we derive existence and uniqueness results for invariant measures of the local equation and infinite SDE system. This machinery is put to use in two examples. First, we give a detailed analysis of the surprisingly subtle case of linear coefficients, which yields a new way to derive the famous Kesten-McKay law for the spectral measure of the regular tree. Second, we construct solutions of tree-indexed SDE systems with nearest-neighbor repulsion effects, similar to Dyson’s Brownian motion.

Staggered quantum phases of dipolar bosons at finite temperatures

The extended Bose-Hubbard model with correlated tunneling exhibits staggered superfluid and supersolid quantum phases. We study finite-temperature phase transitions of quantum phases of dipolar bosons in a two-dimensional optical lattice using Gutzwiller mean-field and quantum Monte Carlo approaches. When nearest-neighbor repulsion is comparable to the on-site interaction, we find that the two topologically distinct superfluids are separated by a normal-fluid phase, while at stronger off-site interactions, density-modulated insulating quantum phases appear. We estimate the critical temperature of the staggered-superfluid to normal-fluid transition and show that this transition is of the Kosterlitz-Thouless type. Finally, we elucidate the coexistence of staggered quantum phases in the presence of an external trapping potential. Our study paves the way to observe novel staggered quantum phases in dipolar optical lattice experiments.

Bridging quantum many-body scars and quantum integrability in Ising chains with transverse and longitudinal fields

Quantum many-body scar (QMBS) and quantum integrability (QI) have been recognized as two distinct mechanisms for the breakdown of eigenstate thermalization hypothesis (ETH) in an isolated system. In this paper, we reveal a smooth route to connect these two ETH-breaking mechanisms in the Ising chain with transverse and longitudinal fields. Specifically, starting from an initial Ising antiferromagnetic state, we find that the dynamical system undergoes a smooth nonthermal crossover from QMBS to QI by changing the Ising coupling ($J$) and longitudinal field ($h$) simultaneously while keeping their ratio fixed, which corresponds to the Rydberg Hamiltonian with an arbitrary nearest-neighbor repulsion. Deviating from this ratio, we further identify a continuous thermalization trajectory in the ($h,J$) plane that is exactly given by the Ising transition line, signifying an intimate relation between thermalization and quantum critical point. Finally, we map out a completely different dynamical phase diagram starting from an initial ferromagnetic state, where the thermalization is shown to be equally facilitated by the resonant spin flip at special ratios of $J$ and $h$. By bridging QMBS and QI in Ising chains, our results demonstrate the breakdown of ETH in much broader physical settings, which also suggest an alternative way to characterize quantum phase transition via thermalization in nonequilibrium dynamics.

Local magnetic moments due to loop currents in metals

We present Hartree-Fock calculations on a simple model to obtain the conditions of formation of local magnetic moments due to loop currents ${L}_{o}$ and spin-loop currents ${L}_{s}$ and compare them to the conditions of formation of local spin moments $M$ which were given long ago in a similar approximation by Anderson. A model with three degenerate orbitals sitting on an equilateral triangle, with on-site and nearest-neighbor repulsions $U$ and $V$, respectively, and intersite kinetic energy, hybridizing with conduction electrons with a parameter $\mathrm{\ensuremath{\Delta}}$ is investigated. ${L}_{o}$ and ${L}_{s}$ are promoted by large $V/\mathrm{\ensuremath{\Delta}}$ and their magnitude is relatively unaffected by $U/\mathrm{\ensuremath{\Delta}}$. Spin-magnetic moments $M$ promoted by large $U/\mathrm{\ensuremath{\Delta}}$ on the other hand are adversely affected by $V/\mathrm{\ensuremath{\Delta}}$. In this model, ${L}_{o}$ for $V$ multiplied by the number of neighbors is approximately the same as the $M$ promoted by $U$ in Anderson's local model for $M$. ${L}_{o}$ and ${L}_{s}$ are degenerate if exchange interactions and Hund's rule are neglected but ${L}_{o}$ is favored when they are included. Many of the qualitative results are visible in an expression for the Hartree-Fock ground state energy derived as a function of small ${L}_{o}, {L}_{s}$, and $M$. Numerical minimization of the Hartree-Fock energy is presented for larger values. We also briefly discuss the connection and differences of the interaction-generated orbital currents and spin currents discussed here and generalized to a lattice with the topological states in metals and semiconductors.

Charge density waves in kagome-lattice extended Hubbard models at the van Hove filling

The Hubbard model on the kagome lattice is presently often considered as a minimal model to describe the rich low-temperature behavior of $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ compounds (with $A=\mathrm{K},\mathrm{Rb},\mathrm{Cs}$), including charge density waves (CDWs), superconductivity, and possibly broken time-reversal symmetry. Here, we investigate, via variational Jastrow-Slater wave functions, the properties of its ground state when both on-site $U$ and nearest-neighbor $V$ Coulomb repulsions are considered at the van Hove filling. Our calculations reveal the presence of different interaction-driven CDWs and, contrary to previous renormalization-group studies, the absence of ferromagnetism and charge- or spin-bond order. No signatures of chiral phases are detected. Remarkably, the CDWs triggered by the nearest-neighbor repulsion possess charge disproportionations that are not compatible with the ones observed in $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$. As an alternative mechanism to stabilize charge-bond order, we consider the electron-phonon interaction, modeled by coupling the hopping amplitudes to quantum phonons, as in the Su-Schrieffer-Heeger model. Our results show the instability towards a trihexagonal distortion with $2\ifmmode\times\else\texttimes\fi{}2$ periodicity, in closer agreement with experimental findings.

Integer quantum Hall effect of two-component hard-core bosons in a topological triangular lattice

We study the many-body ground states of two-component hardcore bosons in topological triangular lattice models. Utilizing exact diagonalization and density-matrix renormalization group calculations, we demonstrate that at commensurate two-thirds filling per lattice site, two-component bosonic integer quantum hall (BIQH) effect emerges with the associated $\mathbf{K}=\begin{pmatrix} 0 & 1\\ 1 & 0\\ \end{pmatrix}$ matrix under strong intercomponent Hubbard repulsion. The topological nature is further elucidated by (i) a unique ground state degeneracy with a robust spectrum gap, (ii) a quantized topological Chern number matrix $\mathbf{C}=\mathbf{K}^{-1}$, and (iii) two counterpropagating edge branches. Moreover, with increasing nearest-neighbor repulsions, the ground state undergoes a first-order transition from a BIQH liquid to a commensurate solid order.

Charge, bond, and pair density wave orders in a strongly correlated system

The coexistence of multiple quasi-degenerate orders is the hallmark of the strongly correlated materials. Experiments often reveal several spatially modulated orders in the underdoped cuprates. This has come to the forefront with the possible detection of the pair density wave states. However, microscopic calculations often struggle to stabilize such spatially modulating orders as the ground state in the strong correlation limit. This work uses the $t-t^\prime-J$-model with an additional nearest-neighbor repulsion to stabilize spatially oscillating charge, bond, and pairing orders in the underdoped regime. We employ the standard Gutzwiller approach while treating the inhomogeneity for the spatial orders using the self-consistent Hartree-Fock-Bogoliubov methodology. Our calculations reveal that unidirectional bond density states coexisting with charge and pairing modulations can have lower energy than the uniform superconducting state over an extensive doping range. These modulating states vanish monotonically as the modulation wavevector becomes shorter with increased dopings. The finite momentum orders melt upon increasing doping to a vestigial nematic state which breaks the rotational symmetry of the system. The spatial features of the ground state at each doping reveal multiple wavevectors, which potentially drives the incommensuration of charge orders. Interestingly, the spatially modulating states are absent when the strong correlations criteria are relaxed, suggesting that the removal of double occupancy aids the stabilization of density wave orders.

From steady-state TASEP model with open boundaries to 1D Ising model at negative fugacity

We expose a series of exact mappings between particular cases of four statistical physics models: (i) equilibrium 1D lattice gas with nearest-neighbor repulsion, (ii) (1 + 1)D combinatorial heap of pieces, (iii) directed random walks on a half-plane, and (iv) 1D totally asymmetric simple exclusion process (TASEP). In particular, we show that generating function of a 1D steady-state TASEP with open boundaries can be interpreted as a quotient of partition functions of 1D hard-core lattice gases with one adsorbing lattice site and negative fugacity. This result is based on the combination of a representation of a steady-state TASEP configurations in terms of (1 + 1)D heaps of pieces (HP) and a theorem of X Viennot which projects the partition function of (1 + 1)D HP onto that of a single layer of pieces, which in this case is a 1D hard-core lattice gas.

Self-generated quantum gauge fields in arrays of Rydberg atoms

As shown in recent experiments (Lienhard et al 2020 Phys. Rev. X 10 021031), spin–orbit coupling in systems of Rydberg atoms can give rise to density-dependent Peierls phases in second-order hoppings of Rydberg spin excitations and nearest-neighbor repulsion. We here study theoretically a one-dimensional zig-zag ladder system of such spin–orbit coupled Rydberg atoms at half filling. The second-order hopping is shown to be associated with an effective gauge field, which in mean-field approximation is static and homogeneous. Beyond the mean-field level the gauge potential attains a transverse quantum component whose amplitude is dynamical and linked to density modulations. We here study the effects of this to the possible ground-state phases of the system. In a phase where strong repulsion leads to a density wave, we find that as a consequence of the induced quantum gauge field a regular pattern of current vortices is formed. However also in the absence of density–density interactions the quantum gauge field attains a non-vanishing amplitude. Above a certain critical strength of the second-order hopping the energy gain due to gauge-field induced transport overcomes the energy cost from the associated build-up of density modulations leading to a spontaneous generation of the quantum gauge field.

Scaling theory of few-particle delocalization

We develop a scaling theory of interaction-induced delocalization of few-particle states in disordered quantum systems. In the absence of interactions, all single-particle states are localized in $d<3$, while in $d \geq 3$ there is a critical disorder below which states are delocalized. We hypothesize that such a delocalization transition occurs for $n$-particle bound states in $d$ dimensions when $d+n\geq 4$. Exact calculations of disorder-averaged $n$-particle Greens functions support our hypothesis. In particular, we show that $3$-particle states in $d=1$ with nearest-neighbor repulsion will delocalize with $W_c \approx 1.4t$ and with localization length critical exponent $\nu = 1.5 \pm 0.3$. The delocalization transition can be understood by means of a mapping onto a non-interacting problem with symplectic symmetry. We discuss the importance of this result for many-body delocalization, and how few-body delocalization can be probed in cold atom experiments.

Competition between spin density wave and charge density wave driven by interactions of spinful Haldane model on honeycomb lattices

We investigate the interacting spinful Haldane model with on-site and nearest-neighbor repulsions on honeycomb lattices. Interactions drive spin-density and charge-density waves competing with each other. This competition enriches the phase diagram of the system greatly, where both topological and non-topological coexistence phases emerge with spin-density and charge-density wave orders. Moreover, the topological phase transition accompanied by the energy gap closure in coexistence phases is of third order. Finally, we study the topological properties consisting of Chern numbers and edge states for different phases.

Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling

Motivated by recent discovery of correlated insulating and superconducting behavior in twisted bilayer graphene, we revisit graphene's honeycomb lattice doped close to the van Hove singularity, using the truncated unity functional renormalization group approach. We consider an extended Hubbard model on the honeycomb lattice including on-site and nearest-neighbor Coulomb repulsions, and nearest-neighbor ferromagnetic exchange and pair hopping interactions. By varying the strength of the nearest-neighbor exchange coupling and Coulomb repulsion as free parameters, we present rich ground-state phase diagrams which contain the spin-triplet $f$-wave and spin-singlet chiral $d$-wave superconducting phases, the commensurate and incommensurate spin- and charge-density-wave phases, and the ferromagnetic phase. In the absence of the exchange coupling and for small value of the nearest-neighbor repulsion, the four-sublattice spin-density-wave phase is generated right around the van Hove filling, while the chiral $d$-wave superconductivity emerges slightly away from it. Surprisingly, the chiral $d$-wave superconductivity is strongly suppressed by weak nearest-neighbor exchange coupling in our calculations. We argue that this suppression might be one of the reasons why the chiral superconductivity proposed for doped graphene has not yet been observed experimentally.

Effective narrow ladder model for two quantum wires on a semiconducting substrate

We present a theoretical study of two spinless fermion wires coupled to a three dimensional semiconducting substrate. We develop a mapping of wires and substrate onto a system of two coupled two-dimensional ladder lattices using a block Lanczos algorithm. We then approximate the resulting system by narrow ladder models, which can be investigated using the density-matrix renormalization group method. In the absence of any direct wire-wire hopping we find that the substrate can mediate an effective wire-wire coupling so that the wires could form an effective two-leg ladder with a Mott charge-density-wave insulating ground state for arbitrarily small nearest-neighbor repulsion. In other cases the wires remain effectively uncoupled even for strong wire-substrate hybridizations leading to the possible stabilization of the Luttinger liquid phase at finite nearest-neighbor repulsion as found previously for single wires on substrates. These investigations show that it may be difficult to determine under which conditions the physics of correlated one-dimensional electrons can be realized in arrays of atomic wires on semiconducting substrates because they seem to depend on the model (and consequently material) particulars.

Bogoliubov-Fermi surface with inversion symmetry and electron-electron interactions: Relativistic analogies and lattice theory

We show that the general low-energy Bogoliubov-de Genness Hamiltonian in a multiband superconductor with broken time reversal and preserved inversion symmetry is a generator of real four-dimensional representation of $SO(4)$. In the particular representation such an effective Hamiltonian is a purely imaginary matrix, and it is proportional to the antisymmetric tensor of a fictitious electromagnetic field which one can define in the momentum space. The quantum time evolution of the low-energy quasiparticle state becomes this way closely related to the classical relativistic motion of a charged particle in the presence of the Lorentz force that would be derived from such an electromagnetic field configuration. The condition for the emergence of a Bogoliubov-Fermi surface can then be understood as orthogonality of the fictitious electric and magnetic fields, which would allow zero Lorentz force. The corresponding zero-energy eigenstates are identified as the physical timelike and the unphysical spacelike solutions of the Lorentz force equation. We study the looming instability of the inversion-symmetric Bogoliubov-Fermi surface in presence of electron-electron interaction by formulating a concrete interacting model on the Lieb lattice that features the requisite $SO(4)$ kinetic energy term together with nearest-neighbor two-body repulsion. The latter is shown to favor dynamical breaking of the inversion symmetry. The inversion symmetry in our lattice model indeed becomes spontaneously broken at zero temperature at infinitesimal repulsion, with the original Bogoliubov-Fermi surface deformed and reduced in size. General features of this symmetry breaking phenomenon are discussed and a comparison with other works in literature is presented.