Hard-core Bosons Research Articles

Dynamics of hard-core bosons in one-dimensional harmonic potential with a periodic monochromatic drive

Dynamics of hard-core bosons in one-dimensional harmonic potential with a periodic monochromatic drive

Evolution of many-body systems under ancilla quantum measurements

Measurement-induced phase transitions are the subject of intense current research, both from an experimental and a theoretical perspective. We explore the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom (implemented using two additional sites), on which projective measurements are performed. We analyze the effect of repeated (``stroboscopic'') measurements on the dynamical correlations of interacting hard-core bosons in a one-dimensional chain. An important distinctive ingredient of the protocol is the fact that the detector ancillae are not reinitialized after each measurement step. The detector thus maintains memory of the accumulated influence by the measured correlated system. Initially, we consider a model in which the ancilla is coupled to a single lattice site. This setup allows obtaining information about the system through Rabi oscillations in the ancillary degrees of freedom, modulated by the ancilla-system interaction. The statistics of quantum trajectories exhibits a ``quantum-Zeno-valve effect'' that occurs when the measurement becomes strong, with sharp branching between low and high entanglement. We proceed by extending numerical simulations to the case of two ancillae and, then, to measurements on all sites. With this realistic measurement apparatus, we find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models. The dynamics features a broad distribution of the entanglement entropy.

Transversal effects on the ground state of hard-core dipolar bosons in one-dimensional optical lattices

Polar lattice gases are usually assumed to have an intersite interaction that decays with the interparticle distance $r$ as $1/{r}^{3}$. However, a loose-enough transversal confinement may strongly modify the dipolar decay in one-dimensional lattices. We show that this modification alters significantly the ground-state properties of hard-core dipolar bosons. For repulsive intersite interactions, the corrected decay alters the conditions for devil's staircase insulators, affecting significantly the particle distribution in the presence of an overall harmonic confinement. For attractive interactions, it results in a reduction of the critical dipole interaction for the formation of self-bound clusters, and for a marked enhancement of the region of liquefied lattice droplets.

Flat bands with high Chern numbers and multiple flat bands in multifold staggered-flux models

Topological flat bands (TFBs) have been proposed in Chern-insulator lattice models. Some two-dimensional monolayer systems can host TFBs with the Chern number $|\mathcal{C}|=1$, and some TFBs with higher Chern numbers are achieved in multilayer or multicomponent systems. In this work, we construct a series of TFBs with higher Chern numbers in the monolayer star lattice by adding several distant-neighbor hopping terms with staggered magnetic fluxes. By considering the third and the fourth nearest-neighbor hopping terms, we find the $|\mathcal{C}|=2$ and $|\mathcal{C}|=3$ TFBs with large flatness ratios, respectively. We also obtain the $|\mathcal{C}|=4$ and $|\mathcal{C}|=5$ TFBs when the fifth and the sixth nearest-neighbor hopping terms are added. Intriguingly, we also observe multiple flat bands with various Chern numbers by tuning the distant-neighbor hopping amplitudes and the staggered-flux parameters. Furthermore, a series of fractional Chern insulator (FCI) states have been numerically observed when hard-core bosons are filled into these TFB models, with fractional fillings $\ensuremath{\nu}=1/3, 2/5, 3/7$ and $\ensuremath{\nu}=1/4, 2/7$ in the $|\mathcal{C}|=2$ and $|\mathcal{C}|=3$ TFBs, respectively. Our findings provide an approach to search for more TFBs with higher Chern numbers and further investigate more interesting FCIs.

Unitary matrix integrals, symmetric polynomials, and long-range random walks

Unitary matrix integrals over symmetric polynomials play an important role in a wide variety of applications, including random matrix theory, gauge theory, number theory, and enumerative combinatorics. We derive novel results on such integrals and apply these and other identities to correlation functions of long-range random walks (LRRW) consisting of hard-core bosons. We generalize an identity due to Diaconis and Shahshahani which computes unitary matrix integrals over products of power sum polynomials. This allows us to derive two expressions for unitary matrix integrals over Schur polynomials, which can be directly applied to LRRW correlation functions. We then demonstrate a duality between distinct LRRW models, which we refer to as quasi-local particle-hole duality. We note a relation between the multiplication properties of power sum polynomials of degree n and fermionic particles hopping by n sites. This allows us to compute LRRW correlation functions in terms of auxiliary fermionic rather than hard-core bosonic systems. Inverting this reasoning leads to various results on long-range fermionic models as well. In principle, all results derived in this work can be implemented in experimental setups such as trapped ion systems, where LRRW models appear as an effective description. We further suggest specific correlation functions which may be applied to the benchmarking of such experimental setups.

Role of interaction-induced tunneling in the dynamics of polar lattice bosons

Intersite dipolar interactions induce, even in absence of disorder, an intriguing nonergodic dynamics for dipolar bosons in an optical lattice. We show that the inherent dipole-induced density-dependent tunneling, typically neglected, plays a crucial role in this dynamics. For shallow-enough lattices, the delocalization stemming from the interaction-induced hopping overcomes the localization induced by intersite interactions. As a result, in stark contrast to the more studied case of hard-core bosons, delocalization is counterintuitively strengthened when the dipolar strength increases. Furthermore, the quasicancellation between bare and interaction-induced tunneling may lead, near a lattice-depth-dependent value of the dipole strength, to an exact decoupling of the Hilbert space between ergodic hard-core states and strongly nonergodic soft-core ones. Our results show that interaction-induced hopping should play a crucial role in future experiments on the dynamics of polar lattice gases.

Composite-boson formalism applied to strongly bound fermion pairs in a one-dimensional trap

We analyze a system of fermions in a one dimensional harmonic trap with attractive delta-interactions between different fermions species, as an approximate description of experiments involving atomic dimers. We solve the problem of two fermion pairs numerically using the so-called "coboson formalism" as an alternative to techniques which are based on the single-particle basis. This allows us to explore the strongly bound regime, approaching the limit of infinite attraction in which the composite particles behave as hard-core bosons. Our procedure is computationally inexpensive and illustrates how the coboson toolbox is useful for ultracold atom systems even in absence of condensation.

Anomalous relaxation of density waves in a ring-exchange system.

We present the analysis of the slowing down exhibited by stochastic dynamics of a ring-exchange model on a square lattice, by means of numerical simulations. We find the preservation of coarse-grained memory of initial state of density-wave types for unexpectedly long times. This behavior is inconsistent with the prediction from a low frequency continuum theory developed by assuming a mean-field solution. Through a detailed analysis of correlation functions of the dynamically active regions, we exhibit an unconventional transient long ranged structure formation in a direction which is featureless for the initial condition, and argue that its slow melting plays a crucial role in the slowing-down mechanism. We expect our results to be relevant also for the dynamics of quantum ring-exchange dynamics of hard-core bosons and more generally for dipole moment conserving models.

Quantum spin liquids of Rydberg excitations in a honeycomb lattice induced by density-dependent Peierls phases

We show that the nonlinear transport of bosonic excitations in a two-dimensional honeycomb lattice of spin-orbit-coupled Rydberg atoms gives rise to disordered quantum phases which are topological and may be candidates for quantum spin liquids. As recently demonstrated by Lienhard et al. [Phys. Rev. X 10, 021031 (2020)] the spin-orbit coupling breaks time-reversal and chiral symmetries and leads to a tunable density-dependent complex hopping of spin excitations which behave as hard-core bosons. Using exact diagonalization (ED), we numerically investigate the phase diagram resulting from the competition between density-dependent and direct transport terms as well as density-density interactions. In mean-field approximation there is a phase transition from a condensate to a ${120}^{\ensuremath{\circ}}$ phase when the amplitude of the complex hopping exceeds that of the direct one. In the full model a new phase emerges close to the mean-field critical point as a result of quantum correlations induced by the density dependence of the complex hopping. We show that without density-density interactions this phase is a genuine disordered one, has large spin chirality, and is characterized by a nontrivial many-body Chern number. The Chern number is found to be robust to disorder. ED simulations of small lattices with up to 30 lattice sites give indications for a nondegenerate ground state with finite spin and collective gaps and thus for a bosonic integer quantum Hall phase, protected by $\mathrm{U}(1)$ symmetry. On the other hand, while staying finite, the many-body gap varies substantially when different twisted boundary conditions are applied, which points to a gapless phase. For very strong negative nonlinear hopping amplitudes we find another disordered regime with vanishing spin gap. This phase also has a large spin chirality and could be a gapless spin liquid but lies outside the parameter regime experimentally accessible in the Rydberg system.

Bose-Hubbard triangular ladder in an artificial gauge field

We consider interacting bosonic particles on a two-leg triangular ladder in the presence of an artificial gauge field. We employ density matrix renormalization group numerical simulations and analytical bosonization calculations to study the rich phase diagram of this system. We show that the interplay between the frustration induced by the triangular lattice geometry and the interactions gives rise to multiple chiral quantum phases. Phase transitions between superfluid to Mott-insulating states occur, which can have Meissner or vortex character. Furthermore, a state that explicitly breaks the symmetry between the two legs of the ladder, the biased chiral superfluid, is found for values of the flux close to $\ensuremath{\pi}$. In the regime of hard-core bosons, we show that the extension of the bond order insulator beyond the case of the fully frustrated ladder exhibits Meissner-type chiral currents. We discuss the consequences of our findings for experiments in cold atomic systems.

Effects of long-range inter-particle interactions and isolated defect on quantum walks of two hard-core bosons in one-dimensional lattices

The quantum walk of two hard-core bosons in one-dimensional lattice under the effect of long-range inter-particle interaction is studied in detail. We also simulate the influence of an isolated defect that may exist in the lattice on the quantum walk of two particles by adding an additional potential energy to a certain lattice site. Using exact diagonalization method, the continuous-time quantum walk is directly simulated. The numerical simulations show that the range of interaction (long-range or short-range), the strength of the inter-particle interaction, the initial state of the two particles and the presence of the isolated defect have great influences on the quantum walk. Under the effect of strong long-range interaction, the particles initially located on the non-adjacent lattice sites have a co-walking behavior, while under the short-range interactions (nearest-neighbor interactions) only two particles initially located on the neighboring lattice sites can exhibit co-walking. After introducing the isolated defect into the system with strong interaction, two particles residing on the same side of the isolated defect keep co-walking, while two particles located on either sides of the isolated defect or one particle located on the isolated defect and the other particle staying on the side of the isolated defect, the two particles keep stationary or co-walking near the defect, displaying the characteristics of localization. By using the second-order perturbation theory of degenerate quantum system, a comprehensive theoretical analysis of the above numerical results is given. The theoretical analysis reveals the underlying physical law of quantum walks of two particles in one-dimensional lattice under the effects of strong long-range interaction and isolated defect in the lattice.

Normal and abnormal thermalization indicators in a one-dimensional low-density Jaynes-Cummings Hubbard model with and without dipole-dipole interaction.

In the one-dimensional low-density Jaynes-Cummings Hubbard (JCH) model, we find that when the hopping strength is much smaller than the coupling strength, the average restricted energy gap ratio exhibits an abnormal statistical behavior that is neither a Poisson nor a Gaussian orthogonal ensemble. But the average half-chain entanglement entropy exhibits ergodicity, and the eigenstate thermalization hypothesis (ETH) is valid for the observable. These results are quite different from those of the standard JCH model. In addition, when the hopping and the coupling strengths are of the same order, quantum chaos still appears in the low-density JCH model, which is in contrast to the integrability of the one-dimensional hard-core bosons. Finally, the dipole-dipole interaction breaks the particle-hole symmetry and leads the abnormal statistical properties to be closer to those of the integrable system at the weak hopping strength limit, but the quantum chaos properties cannot be affected when the hopping strength is of the same order as the coupling strength. Our results demonstrate the counterintuitive behavior in the low-density JCH model and explain the physics behind them from the perspective of the energy spectrum.

Tensor network investigation of the hard-square model

Using the corner-transfer matrix renormalization group to contract the tensor network that describes its partition function, we investigate the nature of the phase transitions of the hard-square model, one of the exactly solved models of statistical physics for which Baxter has found an integrable manifold. The motivation is twofold: assess the power of tensor networks for such models, and probe the 2D classical analog of a 1D quantum model of hard-core bosons that has recently attracted significant attention in the context of experiments on chains of Rydberg atoms. Accordingly, we concentrate on two planes in the 3D parameter space spanned by the activity and the coupling constants in the two diagonal directions. We first investigate the only case studied so far with Monte Carlo simulations, the case of opposite coupling constants. We confirm that, away and not too far from the integrable 3-state Potts point, the transition out of the period-3 phase appears to be unique in the Huse-Fisher chiral universality class, albeit with significantly different exponents as compared to Monte Carlo. We also identify two additional phase transitions not reported so far for that model, a Lifshitz disorder line, and an Ising transition for large enough activity. To make contact with 1D quantum models of Rydberg atoms, we then turn to a plane where the ferromagnetic coupling is kept fixed, and we show that the resulting phase diagram is very similar, the only difference being that the Ising transition becomes first-order through a tricritical Ising point, in agreement with Baxter's prediction that this plane should contain a tricritical Ising point, and in remarkable, almost quantitative agreement with the phase diagram of the 1D quantum version of the model.

Quantum criticality in interacting bosonic Kitaev-Hubbard models

Motivated by recent work on the non-Hermitian skin effect in the bosonic Kitaev-Majorana model, we study the quantum criticality of interacting bosonic Kitaev-Hubbard models on a chain and a two-leg ladder. In the hard-core limit, we show exactly that the non-Hermitian skin effect disappears via a transformation from hard-core bosonic models to spin-1/2 models. We also show that hard-core bosons can engineer the Kitaev interaction, the Dzyaloshinskii-Moriya interaction and the compass interaction in the presence of the complex hopping and pairing terms. Importantly, quantum criticalities of the chain with a three-body constraint and unconstrained soft-core bosons are investigated by the density matrix renormalization group method. This work reveals the effect of many-body interactions on the non-Hermitian skin effect and highlights the power of bosons with pairing terms as a probe for the engineering of interesting models and quantum phase transitions.

Gradient corrections to the local-density approximation in the one-dimensional Bose gas

The local density approximation (LDA) is the central technical tool in the modeling of quantum gases in trapping potentials. It consists in treating the gas as an assembly of independent mesoscopic fluid cells at equilibrium with a local chemical potential, and it is justified when the correlation length is larger than the size of the cells. The LDA is often regarded as a crude approximation, particularly in the ground state of the one-dimensional (1D) Bose gas, { where the correlation length is "therefore said to be" infinite (in the sense that correlation functions decay as a power law).} Here we take another look at the LDA. The local density $\rho(x)$ is viewed as a functional of the trapping potential $V(x)$, to which one applies a gradient expansion. The zeroth order in that expansion is the LDA. The first-order correction in the gradient expansion vanishes due to reflection symmetry. At second order, there are two corrections proportional to $d^2V/dx^2$ and $(dV/dx)^2$, and we propose a method to determine the corresponding coefficients by a perturbative calculation in the Lieb-Liniger model. This leads to an expression for the coefficients in terms of matrix elements of the density operator, which can in principle be evaluated numerically for an arbitrary coupling constant; here we show how to efficiently evaluate the coefficient associated to the curvature of the potential $d^2V/dx^2$, which dominates the deviation to LDA near local minima or maxima of the trapping potential. Both coefficients are evaluated analytically in the limits of infinite repulsion (hard-core bosons) and small repulsion (quasi-condensate).} The corrected LDA density profiles are compared to DMRG calculations, with significant improvement compared to zeroth-order LDA.

Beyond Hard-Core Bosons in Transmon Arrays

Arrays of transmons have proven to be a viable medium for quantum information science and quantum simulations. Despite their widespread popularity as qubit arrays, there remains yet untapped potential beyond the two-level approximation or, equivalently, the hard-core boson model. With the higher excited levels included, coupled transmons naturally realize the attractive Bose-Hubbard model. The dynamics of the model has been difficult to study due to unfavorable scaling of the dimensionality of the Hilbert space with the system size. In this work, we present a framework for describing the effective unitary dynamics of highly-excited states of coupled transmons based on high-order degenerate perturbation theory. This allows us to describe various collective phenomena -- such as bosons stacked onto a single site behaving as a single particle, edge-localization, and effective longer-range interactions -- in a unified, compact and accurate manner. While our examples deal with one-dimensional chains of transmons for the sake of clarity, the theory can be readily applied to more general geometries.

Braiding properties of worldline configurations in hardcore lattice bosons

In this manuscript, we study braiding properties of worldline configurations for a variety of ground-states of hardcore Bose–Hubbard models in two dimensions. Configurations are collections of particle paths and result from the path-integral formulation of statistical mechanics. For hard-core bosons, configurations can be seen as geometric braids and therefore can be assigned a certain topological structure, i.e. a way to classify braiding events among worldlines. By means of Monte Carlo calculations, we study superfluid phase and a variety of insulating phases and observe that ground-states of different quantum phases correspond to different probability distributions of braiding properties.

Static and dynamical Stark many-body localization transition in a linear potential

We investigate hard-core bosons filled in a lattice chain in the presence of a weak linear potential. In the single-particle case, we find that the critical point of dynamical Stark localization is different from that of static Stark localization. This suggests an intermediate phase in which the eigenstates are Stark-localized, but the dynamic wave functions are extended after quenching. In the many-body case, by comparing the dynamical critical point with the static critical point, we find a many-body intermediate phase that is analogous to the single-particle intermediate phase. Furthermore, we also study the static transition for the ground state and the dynamical transition for domain-wall states. In the ground state, we find that the localization transition point is at $V\ensuremath{\approx}2(U+W)$ for half-filling ($U$ is the nearest-neighbor interaction strength, $W$ is the half-bandwidth). For the typical domain-wall state $|111\ensuremath{\cdots}000\ensuremath{\rangle}$, its dynamical transition points are at $V\ensuremath{\approx}4(U+W)$ and $V\ensuremath{\approx}4(U\ensuremath{-}W)$. By analyzing the distribution of the occupation, we also offer a phenomenological way to estimate the above transition points.

Phase diagram of Rydberg-dressed atoms on two-leg triangular ladders

Dressed Rydberg atoms in optical lattices are a promising platform for the quantum simulation of intriguing phenomena emerging in strongly interacting systems. Relevant to such a setup, we investigate the phase diagram of hard-core bosons in a triangular ladder with next-to-nearest-neighbor interaction along each leg and nearest-neighbors interactions without hopping between the legs. For weak interactions, Abelian bosonization predicts a spin density wave and a fully gapless Luttinger liquid phase. Such liquids transition to a 'spin-locked' cluster Luttinger liquid at strong interactions along each leg, as predicted by cluster bosonization. Interestingly, the competition with the zigzag interaction generates a charge density wave, a 'polarized holonic' phase, and a crystalline phase at the filling 2/5, that we address via semi-classical perturbative approach. Exact diagonalization and density matrix renormalization group simulations confirm the predictions and further characterize the phases and their transitions.

Spin-flip-induced superfluidity in a ring of spinful hard-core bosons

The t - J Hamiltonian of the spinful hard-core bosonic ring in the Nagaoka limit is solved. The energy spectrum becomes quantized due to presence of spin, where each energy level corresponds to a cyclic permutation state of the spin chains. The ground state is true ferromagnetic when the ring contains N = 2, 3 spinful hard-core bosons; for all other N it is a mixture of the ferromagnetic and non-ferromagnetic states. This behaviour is different from the fermionic ring, where ground state is true ferromagnetic only for N = 3. It is shown that the intrinsic spin generated gauge fields are analogous to the synthetic gauge fields generated by rotation of either the condensate or the confining potential. It is argued that the low lying excited levels of the spin flipped states intrinsically support the superfluidity. Possible ways to experimentally verify these results are also discussed.