Universal conductivity of dirty bosons at the superconductor-insulator transition

Quantum Criticality at the Superconductor-Insulator Transition Probed by the Nernst Effect

The superconductor-insulator transition (SIT) is an excellent example of a quantum phase transition at zero temperature, dominated by quantum fluctuations. These are expected to be very prominent close to the quantum critical point. So far, most of the experimental studies of the SIT have concentrated on transport properties and tunneling experiments that provide indirect information on criticality close to the transition. Here we present an experiment uniquely designed to study the evolution of quantum fluctuations through the quantum critical point. We utilize the Nernst effect, which has been shown to be effective in probing superconducting fluctuation. We measure the Nernst coefficient in amorphous indium oxide films tuned through the SIT and find a large signal on both the superconducting and the insulating sides, which peaks close to the critical point. The transverse Peltier coefficient α_{xy}, which is the thermodynamic quantity extracted from these measurements, follows quantum critical scaling with critical exponents ν∼0.7 and z∼1. These exponents are consistent with a clean X-Y model in 2+1 dimensions.

Soft Coulomb gap and asymmetric scaling towards metal-insulator quantum criticality in multilayer MoS2

Quantum localization–delocalization of carriers are well described by either carrier–carrier interaction or disorder. When both effects come into play, however, a comprehensive understanding is not well established mainly due to complexity and sparse experimental data. Recently developed two-dimensional layered materials are ideal in describing such mesoscopic critical phenomena as they have both strong interactions and disorder. The transport in the insulating phase is well described by the soft Coulomb gap picture, which demonstrates the contribution of both interactions and disorder. Using this picture, we demonstrate the critical power law behavior of the localization length, supporting quantum criticality. We observe asymmetric critical exponents around the metal-insulator transition through temperature scaling analysis, which originates from poor screening in insulating regime and conversely strong screening in metallic regime due to free carriers. The effect of asymmetric scaling behavior is weakened in monolayer MoS₂ due to a dominating disorder.

The interplay between strong interactions and presence of disorder makes atomically thin transition metal dichalcogenides an ideal platform to study phase transitions and critical phenomena. Here, the authors observe asymmetric critical exponents around the metal-insulator-transition of multilayer MoS₂.

Critical exponents of dynamical conductivity in 2D percolative superconductor-insulator transitions: three universality classes

We simulate three types of random inductor-capacitor (LC) networks on [Formula: see text] square lattices. We calculate the dynamical conductivity using an equation-of-motion method in which timestep error is eliminated and windowing error is minimized. We extract the critical exponent a such that [Formula: see text] at low frequencies. The results suggest that there are three different universality classes. The [Formula: see text] model, with capacitances from each site to ground, has a  =  0.314(4). The [Formula: see text] model, with capacitances along bonds, has a  =  0. The [Formula: see text] model, with both types of capacitances, has a  =  0.304(1). This implies that classical percolative 2D superconductor-insulator transitions (SITs) generically have [Formula: see text] as [Formula: see text]. Therefore, any experiments that give a constant conductivity as [Formula: see text] must be explained in terms of quantum effects.

Critical properties of the superfluid-bose-glass transition in two dimensions

We investigate the superfluid (SF) to Bose-glass (BG) quantum phase transition using extensive quantum Monte Carlo simulations of two-dimensional hard-core bosons in a random box potential. T=0 critical properties are studied by thorough finite-size scaling of condensate and SF densities, both vanishing at the same critical disorder Wc=4.80(5). Our results give the following estimates for the critical exponents: z=1.85(15), ν=1.20(12), η=-0.40(15). Furthermore, the probability distribution of the SF response P(lnρSF) displays striking differences across the transition: while it narrows with increasing system sizes L in the SF phase, it broadens in the BG regime, indicating an absence of self-averaging, and at the critical point P(lnρSF+zlnL) is scale invariant. Finally, high-precision measurements of the local density rule out a percolation picture for the SF-BG transition.

Divergence of dynamical conductivity at certain percolative superconductor-insulator transitions

Random inductor–capacitor (LC) networks can exhibit percolative superconductor-insulator transitions (SITs). We use a simple and efficient algorithm to compute the dynamicalconductivity σ(ω,p) of one type of LC network on large (4000 × 4000) square lattices, where δ = p − p(c) is the tuning parameter for the SIT. We confirm that the conductivity obeys a scaling form, so that the characteristic frequency scales as∝|δ|(νz) with νz ≈ 1.91, the superfluid stiffness scales as ϒ∝|δ|(t) with t ≈ 1.3, and the electric susceptibility scales as χE∝|δ|(−s) with s = 2νz − t ≈ 2.52. In the insulating state, the low-frequency dissipative conductivity is exponentially small, whereas in the superconductor, it is linear in frequency.The sign of Im σ(ω) at small ω changes across the SIT. Most importantly, we find that right at the SIT Re σ(ω) ∝ ω(t/νz−1)∝ω(−0.32), so that the conductivity diverges in the DC limit, in contrast with most other classical and quantum models of SITs.

Quantum critical dynamics simulation of dirty boson systems

Recently, the scaling result z=d for the dynamic critical exponent at the Bose glass to superfluid quantum phase transition has been questioned both on theoretical and numerical grounds. This motivates a careful evaluation of the critical exponents in order to determine the actual value of z. We study a model of quantum bosons at T=0 with disorder in 2D using highly effective worm Monte Carlo simulations. Our data analysis is based on a finite-size scaling approach to determine the scaling of the quantum correlation time from simulation data for boson world lines. The resulting critical exponents are z=1.8±0.05, ν=1.15±0.03, and η=-0.3±0.1, hence suggesting that z=2 is not satisfied.

Universal scaling of the conductivity at the superfluid-insulator phase transition

The scaling of the conductivity at the superfluid-insulator quantum phase transition in two dimensions is studied by numerical simulations of the Bose-Hubbard model. In contrast to previous studies, we focus on properties of this model in the experimentally relevant thermodynamic limit at finite temperature T. We find clear evidence for deviations from omega k scaling of the conductivity towards omega k/T scaling at low Matsubara frequencies omega k. By careful analytic continuation using Padé approximants we show that this behavior carries over to the real frequency axis where the conductivity scales with omega/T at small frequencies and low temperatures. We estimate the universal dc conductivity to be sigma* = 0.45(5)Q2/h, distinct from previous estimates in the T = 0, omega/T >> 1 limit.

Monte Carlo algorithms for charged lattice gases

We consider Monte Carlo algorithms for the simulation of charged lattice gases with purely local dynamics. We study the mobility of particles as a function of temperature and show that the poor mobility of particles at low temperatures is due to "trails" or "strings" left behind after particle motion. We introduce modified updates which substantially improve the efficiency of the algorithm in this regime.

Directed geometrical worm algorithm applied to the quantum rotor model

We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm the Monte Carlo updates are made through the biased reptation of a worm through the lattice. A directed algorithm is an algorithm where, during the construction of the worm, the probability for erasing the immediately preceding part of the worm, when adding a new part, is minimal. We introduce a simple numerical procedure for minimizing this probability. The procedure only depends on appropriately defined local probabilities and should be generally applicable. Furthermore, we show how correlation functions C(r,tau) can be straightforwardly obtained from the probability of a worm to reach a site (r,tau) away from its starting point independent of whether or not a directed version of the algorithm is used. Detailed analytical proofs of the validity of the Monte Carlo algorithms are presented for both the directed and undirected geometrical worm algorithms. Results for autocorrelation times and Green's functions are presented for the quantum rotor model.

Cluster Monte Carlo algorithm for the quantum rotor model

We propose a highly efficient "worm"-like cluster Monte Carlo algorithm for the quantum rotor model in the link-current representation. We explicitly prove detailed balance for the algorithm even in the presence of disorder. For the pure quantum rotor model with mu=0, the algorithm yields high- precision estimates for the critical point K(c)=0.333 05(5) and the correlation length exponent nu=0.670(3). For the disordered case, mu=1 / 2+/-1 / 2, we find nu=1.15(10).

Mott domains of bosons confined on optical lattices

In the absence of a confining potential, the boson-Hubbard model exhibits a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong coupling. We use quantum Monte Carlo simulations to study the ground state of the one-dimensional bosonic Hubbard model in a trap. Some, but not all, aspects of the Mott insulating phase persist. Mott behavior occurs for a continuous range of incommensurate fillings, very different from the unconfined case, and the establishment of the Mott phase does not proceed via a traditional quantum phase transition. These results have important implications for interpreting experiments on ultracold atoms on optical lattices.

Finite-temperature phase diagram of hard-core bosons in two dimensions

We determine the finite-temperature phase diagram of the square lattice hard-core boson Hubbard model with nearest neighbor repulsion using quantum Monte Carlo simulations. This model is equivalent to an anisotropic spin-1/2 XXZ model in a magnetic field. We present the rich phase diagram with a first order transition between a solid and superfluid phase, instead of a previously conjectured supersolid and a tricritical end point to phase separation. Unusual reentrant behavior with ordering upon increasing the temperature is found, similar to the Pomeranchuk effect in 3He.