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arXiv:1909.12168

One-dimensional extended Hubbard model with soft-core potential

Thomas Botzung, Guido Pupillo, Pascal Simon, R. Citro, Elisa Ercolessi

Published Sep 26, 2019• 1 citation
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Abstract

We investigate the $T=0$ phase diagram of a variant of the one-dimensional extended Hubbard model where particles interact via a finite-range soft-shoulder potential. Using Density Matrix Renormalization Group (DMRG) simulations, we evidence the appearance of Cluster Luttinger Liquid (CLL) phases, similarly to what first predicted in a hard-core bosonic chain [M. Mattioli, M. Dalmonte, W. Lechner, and G. Pupillo, Phys. Rev. Lett. 111, 165302]. As the interaction strength parameters change, we find different types of clusters, that encode the order of the ground state in a semi-classical approximation and give rise to different types of CLLs. Interestingly, we find that the conventional Tomonaga Luttinger Liquid (TLL) is separated by a critical line with a central charge $c=5/2$, along which the two (spin and charge) bosonic degrees of freedom (corresponding to $c=1$ each) combine in a supersymmetric way with an emergent fermionic excitation ($c=1/2$). We also demonstrate that there are no significant spin correlations.

DOI
10.48550/arxiv.1909.12168

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We investigate the T=0T=0T=0 phase diagram of a variant of the one-dimensional extended Hubbard model where particles interact via a finite-range soft-shoulder potential. Using Density Matrix Renormalization Group (DMRG) simulations, we evidence the appearance of Cluster Luttinger Liquid (CLL) phases, similarly to what first predicted in a hard-core bosonic chain [M. Mattioli, M. Dalmonte, W. Lechner, and G. Pupillo, Phys. Rev. Lett. 111, 165302]. As the interaction strength parameters change, we find different types of clusters, that encode the order of the ground state in a semi-classical approximation and give rise to different types of CLLs. Interestingly, we find that the conventional Tomonaga Luttinger Liquid (TLL) is separated by a critical line with a central charge c=5/2c=5/2c=5/2, along which the two (spin and charge) bosonic degrees of freedom (corresponding to c=1c=1c=1 each) combine in a supersymmetric way with an emergent fermionic excitation (c=1/2c=1/2c=1/2). We also demonstrate that there are no significant spin correlations.
We investigate the quantum phases of hard-core bosonic atoms in an extended Hubbard model where particles interact via soft-shoulder potentials in one dimension. Using a combination of field-theoretical methods and strong-coupling perturbation theory, we demonstrate that the low-energy phase can be a conformal cluster Luttinger liquid (CLL) phase with central charge c=1c=1c=1, where the microscopic degrees of freedom correspond to mesoscopic ensembles of particles. Using numerical density-matrix renormalization-group methods, we demonstrate that the CLL phase [first predicted in M. Mattioli et al., Phys. Rev. Lett. 111, 165302 (2013)] is separated from a conventional Tomonaga-Luttinger liquid by an exotic critical point with central charge c=32c=\frac{3}{2}c=23​. The latter is expression of an emergent conformal supersymmetry, which is not present in the original Hamiltonian. We discuss the observability of the CLL phase in realistic experimental settings with weakly dressed Rydberg atoms confined to optical lattices. Using quantum Monte Carlo simulations, we show that the typical features of CLLs are stable up to comparatively high temperatures. Using exact diagonalizations and quantum trajectory methods, we provide a protocol for adiabatic state preparation as well as quantitative estimates on the effects of particle losses.
Rydberg and Rydberg-dressed atomic gases have recently emerged as a promising quantum simulator for a variety of models in condensed matter physics. Here we investigate one-dimensional bosons with soft-core Rydberg-dressed interactions using exact path-integral quantum Monte Carlo simulations. The finite-range and the negative Fourier component of the interaction potential generate a roton mode at finite momentum, while particle-hole backscattering processes enhance the susceptibility of one-dimensional systems at twice the Fermi momentum. The competition between the corresponding length scales yields a rich phase diagram, featuring a conventional Tomonaga-Luttinger liquid (TLL) regime, a beyond-TLL regime, and commensurate cluster phases. In the TLL regime, the system transitions from Lieb-Liniger-like bnehavior with Luttinger parameter K>1K>1K>1 to hard-rod-like behavior with K<1K<1K<1, with a quasi-supersolid phase emerging for K<1/2K < 1/2K<1/2. For strong interactions and high densities, deviations from TLL theory appear as precursors for the onset of cluster phases, where particles aggregate into stable clusters of several particles. The properties of each phase is discussed in detail.
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We investigate the zero-temperature phases of bosonic and fermionic gases confined to one dimension and interacting via a class of finite-range soft-shoulder potentials (i.e., soft-core potentials with an additional hard-core onsite interaction). Using a combination of analytical and numerical methods, we demonstrate the stabilization of critical quantum liquids with qualitatively new features with respect to the Tomonaga-Luttinger liquid paradigm. These features result from frustration and cluster formation in the corresponding classical ground state. Characteristic signatures of these liquids are accessible in state-of-the-art experimental setups with Rydberg-dressed ground-state atoms trapped in optical lattices.
The extended Hubbard model in one dimension is studied for half-filled bands using a continuum theory based on the Luttinger model. Interactions going beyond the Luttinger model are treated with a renormalization group. We compute correlation functions and use these to establish the phase diagram of the model. It compares favorably with earlier numerical work. Specifically, we identify additional interaction terms coupling charge and spin degrees of freedom; one of them is shown to mediate the crossover from a continuous to a first-order transition from spin- to charge-density waves at a finite value of U=2V. Our approach suggests viewing the model on this line as two weakly coupled interpenetrating systems of up-spin and down-spin electrons with strong backscattering interactions favoring charge-density waves separately in each of the subsystems. A first-order transition occurring for attractive interactions is interpreted as a characteristic instability of the Luttinger liquid towards phase separation. We finally discuss a possible equivalence to some recent studies of coupled two-dimensional XY models.
One-dimensional free fermions and hard-core bosons are often considered to be equivalent. Indeed, when restricted to nearest-neighbor hopping on a chain, the particles cannot exchange themselves, and therefore hardly experience their own statistics. Apart from the off-diagonal correlations which depend on the so-called Jordan-Wigner string, real-space observables are similar for free fermions and hard-core bosons on a chain. Interestingly, by coupling only two chains, thus forming a two-leg ladder, particle exchange becomes allowed and leads to a totally different physics between free fermions and hard-core bosons. Using a combination of analytical (strong coupling, field theory, renormalization group) and numerical (quantum Monte Carlo, density-matrix renormalization group) approaches, we study the apparently simple but nontrivial model of hard-core bosons hopping in a two-leg ladder geometry. At half filling, while a band insulator appears for fermions at large interchain hopping ${t}_{\ensuremath{\perp}}>2t$ only, a Mott gap opens up for bosons as soon as ${t}_{\ensuremath{\perp}}\ensuremath{\ne}0$ through a Kosterlitz-Thouless transition. Away from half filling, the situation is even more interesting since a gapless Luttinger liquid mode emerges in the symmetric sector with a nontrivial filling-dependent Luttinger parameter $1/2\ensuremath{\leqslant}{K}_{s}\ensuremath{\leqslant}1$. Consequences for experiments in cold atoms and spin ladders in a magnetic field, as well as disorder effects, are discussed. In particular, a quantum phase transition is expected at finite disorder strength between a one-dimensional superfluid and an insulating Bose glass phase.