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arXiv:2310.17682 · Physical review. B./Physical review. B

Scale-invariant phase transition of disordered bosons in one dimension

Tanul Gupta, Guido Masella, Francesco Mattiotti, Nikolay V. Prokof'ev, Guido Pupillo

Published Jan 8, 2025• 3 citations
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Abstract

The disorder-induced quantum phase transition between superfluid and nonsuperfluid states of bosonic particles in one dimension is generally expected to be of the Berezinskii-Kosterlitz-Thouless (BKT) type. Here, we show that hard-core lattice bosons with power-law hopping decaying with distance as $1/{r}^{\ensuremath{\alpha}}$ with a finite integral over space---corresponding in spin language to an $XY$ model with power-law couplings---undergo a non-BKT continuous phase transition instead. We use exact quantum Monte Carlo methods to determine the phase diagram for different values of the exponent $\ensuremath{\alpha}$, focusing on the regime $\ensuremath{\alpha}>2$. We find that the scaling of the superfluid stiffness with the system size is scale invariant at the transition point for any $\ensuremath{\alpha}\ensuremath{\le}3$---a behavior incompatible with the BKT scenario and typical of continuous phase transitions in higher dimension. By a scaling analysis near the transition point, we find that our data are consistent with a correlation length exponent satisfying the Harris bound $\ensuremath{\nu}\ensuremath{\ge}2$ and demonstrate a universal behavior of disordered bosons in one dimension. For $\ensuremath{\alpha}>3$ our data are consistent with a BKT scenario where the liquid is pinned by infinitesimal disorder.

DOI
10.1103/physrevb.111.l020503

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The disorder-induced quantum phase transition between superfluid and nonsuperfluid states of bosonic particles in one dimension is generally expected to be of the Berezinskii-Kosterlitz-Thouless (BKT) type. Here, we show that hard-core lattice bosons with power-law hopping decaying with distance as 1/r\ensuremathα1/{r}^{\ensuremath{\alpha}}1/r\ensuremathα with a finite integral over space---corresponding in spin language to an XYXYXY model with power-law couplings---undergo a non-BKT continuous phase transition instead. We use exact quantum Monte Carlo methods to determine the phase diagram for different values of the exponent \ensuremathα\ensuremath{\alpha}\ensuremathα, focusing on the regime \ensuremathα>2\ensuremath{\alpha}>2\ensuremathα>2. We find that the scaling of the superfluid stiffness with the system size is scale invariant at the transition point for any \ensuremathα\ensuremath≤3\ensuremath{\alpha}\ensuremath{\le}3\ensuremathα\ensuremath≤3---a behavior incompatible with the BKT scenario and typical of continuous phase transitions in higher dimension. By a scaling analysis near the transition point, we find that our data are consistent with a correlation length exponent satisfying the Harris bound \ensuremathν\ensuremath≥2\ensuremath{\nu}\ensuremath{\ge}2\ensuremathν\ensuremath≥2 and demonstrate a universal behavior of disordered bosons in one dimension. For \ensuremathα>3\ensuremath{\alpha}>3\ensuremathα>3 our data are consistent with a BKT scenario where the liquid is pinned by infinitesimal disorder.
We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as 1/r^{α} using exact large scale quantum Monte Carlo simulations. For all 1<α≤3 the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in marked contrast with the Berezinskii-Kosterlitz-Thouless (BKT) scenario that is recovered only for α>3. By performing finite-size scaling collapses of the superfluid stiffness and extracting dynamical and correlation-length exponents from the low-energy spectrum, we establish that these transitions define a distinct universality class throughout the long-range regime 1<α≤3. Analysis of the single-particle correlation functions and grand canonical phase diagram further reveals a sequence of ordering regimes within the superfluid phase: true long-range order for α≤2, anomalous quasi-long-range order for 2<α≤3, and conventional algebraic decay for α>3. Our exact numerical results provide a benchmark to compare theories of long-range quantum models and are relevant for experiments with cold neutral atom, molecules and ion chains.
We present numerical evidence from Monte Carlo simulations that the superfluid-insulator quantum phase transition of interacting bosons subject to strong disorder in one dimension is controlled by the strong-randomness critical point. At this critical point the distribution of superfluid stiffness over disorder realizations develops a power-law tail reflecting a universal distribution of weak links. The Luttinger parameter on the other hand does not take on a universal value at this critical point, in marked contrast to the known Berezinskii-Kosterlitz-Thouless-like superfluid-insulator transition in weakly disordered systems. We develop a finite-size scaling procedure which allows us to directly compare the numerical results from systems of linear size up to 1024 sites with theoretical predictions obtained by Altman et al. [Phys. Rev. Lett. 93, 150402 (2004)] using a strong disorder renormalization group approach. The data shows good agreement with the scaling expected at the strong-randomness critical point.
Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different regimes. At small attraction where critical disorder is weak compared to the bandwidth, the critical Luttinger parameter Kc{K}_{c}Kc​ takes its universal Giamarchi-Schulz value Kc=3/2{K}_{c}=3/2Kc​=3/2. Conversely, a nonuniversal Kc>3/2{K}_{c}>3/2Kc​>3/2 emerges for stronger attraction where weak-link physics is relevant. In this strong-disorder regime, the transition is characterized by self-similar power-law-distributed weak links with a continuously varying characteristic exponent $\ensuremath{\alpha}$.
The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a quasiordered phase, characterized by a power-law scaling of the correlation functions at low temperature, is disrupted by the proliferation of topological excitations above the critical temperature T_{BKT}. In this Letter, we consider the effect of long-range decaying couplings ∼r^{-2-σ} on the BKT transition. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. It features-for 7/4<σ<2-a quasiordered phase in a finite temperature range T_{c}<T<T_{BKT}, which occurs between a symmetry broken phase for T<T_{c} and a disordered phase for T>T_{BKT}. The transition temperature T_{c} displays unique universal features quite different from those of the traditional, short-range XY model. Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems.
We study the phase diagram of two-dimensional, interacting bosons in the presence of a correlated disorder in continuous space, by using large-scale quantum Monte Carlo simulations at finite temperature. We show that the superfluid transition is strongly protected against disorder. It remains of the Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the chemical potential. Moreover, we study the transport properties in the strong disorder regime where a zero-temperature Bose-glass phase is expected. We show that the conductance exhibits a thermally activated behavior vanishing only at zero temperature. Our results point towards the existence of a Bose bad-metal phase as a precursor of the Bose-glass phase.
We study the universal critical behavior of two-dimensional (2D) lattice bosonic gases at the Berezinskii-Kosterlitz-Thouless (BKT) transition, which separates the low-temperature superfluid phase from the high-temperature normal phase. For this purpose, we perform quantum Monte Carlo simulations of the hard-core Bose-Hubbard (BH) model at zero chemical potential. We determine the critical temperature by using a matching method that relates finite-size data for the BH model with corresponding data computed in the classical XYXYXY model. In this approach, the neglected scaling corrections decay as inverse powers of the lattice size LLL, and not as powers of 1/lnL1/\mathrm{ln}L1/lnL, as in more standard approaches, making the estimate of the critical temperature much more reliable. Then, we consider the BH model in the presence of a trapping harmonic potential, and we verify the universality of the trap-size dependence at the BKT critical point. This issue is relevant for experiments with quasi-2D trapped cold atoms.