Scale-invariant phase transition of disordered bosons in one dimension

• URL: http://arxiv.org/abs/2310.17682v1
• Date: Thu, 26 Oct 2023 13:30:12 GMT
• Title: Scale-invariant phase transition of disordered bosons in one dimension
• Authors: Tanul Gupta, Guido Masella, Francesco Mattiotti, Nikolay V. Prokof'ev, and Guido Pupillo
• Abstract summary: disorder-induced quantum phase transition between superfluid and non-superfluid 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 integrable power-law hopping decaying with distance as $1/ralpha$ undergo a non-BKT continuous phase transition instead.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The disorder-induced quantum phase transition between superfluid and non-superfluid 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 integrable power-law hopping decaying with distance as $1/r^\alpha$ - corresponding in spin language to a $XY$ 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 $\alpha$, focusing on the regime $\alpha > 2$. We find that the scaling of the superfluid stiffness with the system size is scale-invariant at the transition point for any $\alpha\leq 3$ - a behavior incompatible with the BKT scenario and typical of continuous phase transitions in higher dimension. By scaling analysis near the transition point, we find that our data are consistent with a correlation length exponent satisfying the Harris bound $\nu \geq 2$ and demonstrate a new universal behavior of disordered bosons in one dimension. For $\alpha>3$ our data are consistent with a BKT scenario where the liquid is pinned by infinitesimal disorder.

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