Superfluid-insulator transition in commensurate disordered bosonic systems: large-scale worm algorithm simulations

We report results of large-scale Monte Carlo simulations of superfluid-insulator transitions in disordered commensurate 2D bosonic systems. In the off-diagonal disorder case, we find that the transition is to a gapless incompressible insulator, and its dynamical critical exponent is z=1.5(2). In the diagonal-disorder case, we prove the conjecture that rare statistical fluctuations are inseparable from critical fluctuations on the largest scales and ultimately result in crossover to the generic universality class (apparently with z=2). However, even at strong disorder, the universal behavior sets in only at very large space-time distances. This explains why previous studies of smaller clusters mimicked a direct superfluid-Mott-insulator transition.     

Perturbation expansion for a one-dimensional Anderson model with off-diagonal disorder

The weak disorder expansion for a random Schrödinger equation with off-diagonal disorder in one dimension is studied. The invariant measure, the density of states, and the Lyapunov exponent are computed. The most interesting feature in this model appears at the band center, where the differentiated density of states diverges, while the Lyapunov exponent vanishes. The invariant measure approaches an atomic measure concentrated on zero and infinity. The results extend previous work of Markos to all orders of perturbation theory.     

Order-disorder transition in one-dimensional system with disorder in composition

The influence of structural inhomogeneity onto order-disorder transitions in 1D systems is considered in the scope of the Potts-like model with many-particle interactions. The helix-coil transition in DNAs, heterogeneous by hydrogen bonding energy, is considered as an example. The microcanonical method is employed to evaluate the free energy. The secular equation for the heteropolymer is constructed. Both the melting temperature and interval of DNA melting are obtained. In the limit of small difference between inverse melting temperatures of poly(A-T) and poly(G-C), the coincidence with classical results is obtained.     

Phase transition in a system of one-dimensional bosons with strong disorder

We study one-dimensional disordered bosons at large commensurate filling. Using a real space renormalization group approach, we find a new random fixed point which controls a phase transition from a superfluid to an incompressible Mott glass. The transition can be tuned by changing the disorder distribution even with vanishing interactions. We derive the properties of the transition, which suggest that it is in the Kosterlitz-Thouless universality class.     

Anderson localization in different one-dimensional systems with off-diagonal disorder and spin-dependence

The localization properties of certain spin-dependent, one-dimensional electronic systems with only off-diagonal disorder are studied. In higher dimensions (d=2,3) the models considered would correspond to different universality classes, whereas ford=1 no qualitative difference is found: ForE=0, all eigenstates are exponentially localized, whereas forE0 the localization length diverges logarithmically, such that exactly atE=0 the geometric average of the transmission coefficient would decay with increasing chain lengthL as exp (-const. ·L ^1/2), instead of the usual, exponential decay.ForE=0, in the interior of the band, the localization lengthr ₀ diverges W ₂ ^–2 in the limit of weak disorder (W ₂0), whereas just at the band edge one has roughlyr ₀W ₂ ^–2/3. A universal recursion relation, depending only on the energy and on certain randomly distributed determinants, determines the localization length and the density of states for all systems considered.     

Current in a quantum driven thermostatted system with off-diagonal disorder

We analyze a one dimensional quantum model with off-diagonal disorder, consisting of a sequence of potential energy barriers whose width is a random variable either uniformly or “half-normally” distributed, subjected to an external electric field. We shed light on how the microscopic disorder affects the value of the transmission coefficient and on the structure of the fluctuations around the solutions corresponding to the regular lattice configuration. We also characterize the asymptotic limit obtained by letting the number of barriers diverge. Thus, we explain the novelty of our method with respect to the standard thermodynamic limit discussed in the literature and also evidence the onset of a large deviation principle for the transmission coefficient.     

Superfluid-insulator transition in a moving system of interacting bosons

We analyze the stability of superfluid currents in a system of strongly interacting ultracold atoms in an optical lattice. We show that such a system undergoes a dynamic, irreversible phase transition at a critical phase gradient that depends on the interaction strength between atoms. At commensurate filling, the phase boundary continuously interpolates between the classical modulation instability of a weakly interacting condensate and the equilibrium quantum phase transition into a Mott insulator state at which the critical current vanishes. We argue that quantum fluctuations smear the transition boundary in low dimensional systems. Finally we discuss the implications to realistic experiments.     

Localization-delocalization transition in one-dimensional system with long-range correlated diagonal disorder

We show that the electronic states in a one-dimensional (1D) Anderson model of diagonal disorder with long-range correlation proposed by de Moura and Lyra exhibit localization-delocalization phase transition in varying the energy of electrons. Using transfer matrix method, we calculate the average resistivity and investigate how it changes with the size of the system N. For given value of α (> 2) we find critical energies E_c1 and E_c2 such that the resistivity decreases with N as a power law ∝ N ^{- γ} for electron energies within the range of [E _c1, E _c2], and exponentially grows with N outside this range. Such behaviors persist in approaching the transition points and the exponent γ is in the range from 0.92 to 0.96. The origin of the delocalization in this 1D model is discussed. Received 18 December 2001 / Received in final form 2 May 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: sjxiong@nju.edu.cn     

Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method

The values of the insulator gap Δ in one-dimensional systems of interacting bosons described by the Hubbard Hamiltonian are calculated at low temperatures by the quantum world-line Monte Carlo algorithm. The dependence of Δ on the size of the system, the temperature, and the parameters of the model is investigated. It is shown that a chain with N _a=50 sites is already sufficient to estimate the thermodynamic value of the critical quantity (t/U)_c for which a transition from the insulator into the superfluid state occurs in a commensurate system. To within the computational error, this value, (t/U)_c=0.300±0.005, agrees with the value (t/U)_c=0.304±0.002 obtained previously by the combined “exact diagonalization + renormalization-group analysis” method. The characteristic Kosterlitz-Thouless behavior of the insulator gap is demonstrated near the critical region: Δ∼exp[−b(1−t/t _c)^−1/2]. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 92–96 (25 July 1996)     

一维二元非对角关联无序体系跳跃电导特性

在单电子紧束缚无序模型基础上，建立了一维二元关联无序体系电子跳跃输运直流电导模型，并推导了其直流电导公式，通过计算其直流电导率，探讨了格点能量无序度、非对角关联及温度、外场对体系跳跃电导的影响.计算结果表明，一维二元无序体系的直流电导率随着格点能量无序度的增大而减小；当引入非对角关联时，体系出现退局域化现象，从而使体系的直流电导率增大；温度对体系的电子输运的影响表现为体系的直流电导率随温度的升高而增大；在外加电场的调制下，体系的直流电导率在强场区随电场强度增加而增长很快，呈现出非欧姆定律特性，但在弱场区外场的作用不明显. 关键词： 二元无序体系 跳跃电导 格点能量无序度 非对角关联     

Coherent electronic dynamics and absorption spectra in an one-dimensional model with long-range correlated off-diagonal disorder

In this work we study an one-dimensional Anderson model with long-range correlated off-diagonal disorder. We numerically demonstrate the presence of extended states and an anomalous optical absorption spectrum for high degrees of correlation. We also show that the electric field biased electronic wave packet dynamics shows Bloch-like oscillations.     

Superfluid-insulator transition in a periodically driven optical lattice

We demonstrate that the transition from a superfluid to a Mott insulator in the Bose-Hubbard model can be induced by an oscillating force through an effective renormalization of the tunneling matrix element. The mechanism involves adiabatic following of Floquet states, and can be tested experimentally with Bose-Einstein condensates in periodically driven optical lattices. Its extension from small to very large systems yields nontrivial information on the condensate dynamics.     

A comment on Anderson's transition in systems with purely off-diagonal disorder

We make a comment on a recent paper by Antoniou and Economou concerning the electron localization in systems with off-diagonal randomness. Particularly, we discuss the validity of the ordinary cluster coherent potential approximation and of the L(E) method, both of which were used as grounds to draw their conclusion.     

CPA conductivity of a binary alloy with off-diagonal disorder

D.c.-conductivity of a binary alloy A_xB_y with off-diagonal disorder is calculated, assuming Shiba's condition for the random transfer integrals, by means of a modified CPA, i.e.,the renormalization propagator formalism developed elsewhere by one of the authors (K.N.).     

一维二元非对角关联无序体系交流跳跃电导特性

在单电子紧束缚无序模型基础上，建立了一维二元非对角关联无序体系电子跳跃输运交流电导模型，并推导了其交流电导公式，通过计算其交流电导率，探讨了格点能量无序度、格点原子组分、非对角关联及温度、外场对体系交流跳跃电导的影响.计算结果表明，一维二元非对角关联无序体系的交流电导率随格点能量无序度的增大而减小.同时，体系中两种原子的组分的变化实际代表着体系成分无序程度的变化，因而对其交流电导率的影响很大，表现为随A类原子含量p的增加而先减小后增大.当引入非对角关联时，体系出现退局域化现象，电子波函数由局 关键词： 二元无序体系 交流跳跃电导 格点能量无序度 非对角关联     

无序度对一维长程关联无序系统中局域化-退局域化转变的影响

对长程幂律关联能量序列进行了修正,使其能体现出无序度在一维长程关联无序系统中的影响,并利用重正化群方法,计算了能反映该系统局域化-退局域化转变的Lyapunov指数.结果表明,在由于关联指数p的影响而在系统中出现的局域化向退局域化的转变中,无序度起着相反的作用.当关联指数p一定而无序度W增大时,系统中心能区范围内由于长程关联而引起的扩展态逐渐向局域态转变.当无序度W增大到某一临界值W_c时,系统中所有本征态均转变为局 关键词： 长程关联 Lyapunov指数 无序度 局域化-退局域化转变