Bose-glass Transition Research Articles

Superfluid–Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension

Superfluid–Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension

Quench spectroscopy of a disordered quantum system

The characterization of excitations in disordered quantum systems is a central issue in connection with glass physics and many-body localization. Here, we show that quench spectroscopy of a disordered model, as realized from its out-of-equilibrium dynamics following a global quench, allows us to fully characterize the spectral properties of the disordered phases. In the Bose-Hubbard model, a clear signature of gapless excitations in momentum-resolved spectroscopy enables us to accurately locate the Mott insulator to Bose glass transition, while the presence or absence of a well-defined soundlike mode distinguishes the superfluid from the Bose glass phase. Moreover, spatially-resolved spectroscopy provides local spectral properties and allows us to extract the typical spacing of gapless regions, giving a second independent way to uniquely identify all three phases. Our findings have far-ranging implications for a variety of experimental platforms, and offer a powerful and versatile probe of the low-energy phases of disordered systems.

Finite-size scaling analysis of localization transitions in the disordered two-dimensional Bose-Hubbard model within the fluctuation operator expansion method

The disordered Bose-Hubbard model in two dimensions at non-integer filling admits a superfluid to Bose-glass transition at weak disorder. Less understood are the properties of this system at strong disorder and energy densities corresponding to excited states. In this work we study the Bose-glass transition of the ground state and the related finite energy localization transition, the mobility edge of the quasiparticle spectrum, a critical energy separating extended from localized quasiparticle excitations. To study these the fluctuation operator expansion is used. The level spacing statistics of the quasiparticle excitations, the fractal dimension and decay of the corresponding wave functions are consistent with a many-body mobility edge. The finite-size scaling of the lowest gaps yields a correction to the mean-field prediction of the superfluid to Bose-glass transition. In its vicinity we discuss spectral properties of the ground state in terms of the dynamic structure factor and the spectral function which also shows distinct behavior above and below the mobility edge.

Lieb-Liniger Bosons in a Shallow Quasiperiodic Potential: Bose Glass Phase and Fractal Mott Lobes.

The emergence of a compressible insulator phase, known as the Bose glass, is characteristic of the interplay of interactions and disorder in correlated Bose fluids. While widely studied in tight-binding models, its observation remains elusive owing to stringent temperature effects. Here we show that this issue may be overcome by using Lieb-Liniger bosons in shallow quasiperiodic potentials. A Bose glass, surrounded by superfluid and Mott phases, is found above a critical potential and for finite interactions. At finite temperature, we show that the melting of the Mott lobes is characteristic of a fractal structure and find that the Bose glass is robust against thermal fluctuations up to temperatures accessible in quantum gases. Our results raise questions about the universality of the Bose glass transition in such shallow quasiperiodic potentials.

Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid–Bose glass transition in one dimension

We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate $1/T_1$ in random one-dimensional spin chains as function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The $1/T_1$ is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter $K$. We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function in order to extract the $1/T_1$ experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.

Weak- versus strong-disorder superfluid—Bose glass transition in one dimension

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 $K_c$ takes its universal Giamarchi-Schulz value $K_{c}=3/2$. Conversely, a non-universal $K_c>3/2$ 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 $\alpha$.

Self-consistent T-matrix approach to Bose-glass in one dimension

Based on the self-consistent T-matrix approximation (SCTMA), the Mott insulator – Bose-glass phase transition of one-dimensional noninteracting bosons subject to binary disorder is considered. The results obtained differ essentially from the conventional case of box distribution of the disorder. The Mott insulator – Bose-glass transition is found to exist at arbitrary strength of the impurities. The single particle density of states is calculated within the frame of SCTMA, numerically, and (for infinite disorder strength) analytically. A good agreement is reported among all three methods. We speculate that certain types of the interaction may lead to the Bose-glass – superfluid transition absent in our theory.

Thermodynamic evidence for the Bose glass transition in twinnedYBa2Cu3O7−δcrystals

We used a micromechanical torsional oscillator to measure the magnetic response of a twinned YBa$_2$Cu$_3$O$_{7-\delta}$ single crystal disk near the Bose glass transition. We observe an anomaly in the temperature dependence of the magnetization consistent with the appearance of a magnetic shielding perpendicular to the correlated pinning of the twin boundaries. This effect is related to the thermodynamic transition from the vortex liquid phase to a Bose glass state.

Magnetic Field of BG-VG Transition Depending on the Nanorods Shape in <inline-formula> <tex-math notation="TeX">$\hbox{BaHfO}_{3}$</tex-math></inline-formula>-Doped <inline-formula> <tex-math notation="TeX">$\hbox{SmBa}_{2}\hbox{Cu}_{3}\hbox{O}_{y}$</tex-math></inline-formula> Films

The vortex state under the magnetic held around vortex glass (VG)-Bose glass (BG) transition held was investigated in the SmBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</sub> (SmBCO) films with BaHfO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> (BHO) nanorods. We prepared two films with different forms of the nanorods (thick-straight and thin-tilted), and we used the magnetic held angular dependence of flux flow resistivity (p - θ) to identify a vortex state. From a comparison between the p - θ curves in completely BG and VG phases, it was revealed that the existence of deep and sharp dip structure along the c-axis direction of the SmBCO matrix (B//c) was an evidence of the BG state in both the films. In the magnetic held region around VG-BG transition, shallower and broader dips than the dips in the BG state were observed at B//c in both the films. In addition, the dips became deeper with increase of the magnetic held in this region in each film. Therefore, we considered the vortex state of both the films was an intermediate and/or a transient state of BG and VG. Under all magnetic fields, the film with thick and straight BHO nanorods showed stronger c-axis correlated flux pinning force than the film with thin and tilted nanorods. We suggested the intermediate state of the hlm with thicker and straighter nanorods was similar to the BG state compared with another hlm from the both of experimental results and reported theory.

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.

Critical exponents of the superfluid-Bose-glass transition in three dimensions.

Recent experimental and numerical studies of the critical-temperature exponent ϕ for the superfluid-Bose-glass universality in three-dimensional systems report strong violations of the key quantum critical relation, ϕ=νz, where z and ν are the dynamic and correlation-length exponents, respectively; these studies question the conventional scaling laws for this quantum critical point. Using MonteCarlo simulations of the disordered Bose-Hubbard model, we demonstrate that previous work on the superfluid-to-normal-fluid transition-temperature dependence on the chemical potential (or the magnetic field, in spin systems), T_{c}∝(μ-μ_{c})^{ϕ}, was misinterpreting transient behavior on approach to the fluctuation region with the genuine critical law. When the model parameters are modified to have a broad quantum critical region, simulations of both quantum and classical models reveal that the ϕ=νz law [with ϕ=2.7(2), z=3, and ν=0.88(5)] holds true, resolving the ϕ-exponent "crisis."

Bose-glass Transition and Spin-Wave Localization for 2D Bosons in a Random Potential

A spin-wave approach of the zero temperature superfluid-insulator transition for two-dimensional hard-core bosons in a random potential μ=±W is developed. While at the classical level there is no intervening phase between the Bose-condensed superfluid (SF) and the gapped disordered insulator, the introduction of quantum fluctuations leads to a much richer physics. Upon increasing the disorder strength W, the Bose-condensed fraction disappears first, before the SF. Then a gapless Bose-glass phase emerges over a finite region until the insulator appears. Furthermore, in the strongly disordered SF regime, a mobility edge in the spin-wave excitation spectrum is found at a finite frequency Ω(c) decreasing with W, and presumably vanishing in the Bose-glass phase.

Noise correlation scalings: Revisiting the quantum phase transition in incommensurate lattices with hard-core bosons

Finite size scalings of the momentum distribution and noise correlations are performed to study Mott insulator, Bose glass, and superfluid quantum phases in hard-core bosons (HCBs) subjected to quasiperiodic disorder. The exponents of the correlation functions at the superfluid to Bose-glass (SF-BG) transition are found to be approximately one half of the ones that characterize the superfluid phase. The derivatives of the peak intensities of the correlation functions with respect to quasiperiodic disorder are shown to diverge at the SF-BG critical point. This behavior does not occur in the corresponding free fermion system, which also exhibits an Anderson-like transition at the same critical point and thus provides a unique experimental tool to locate the phase transition in interacting bosonic systems. We also report on the absence of primary sublattice peaks in the momentum distribution of the superfluid phase for special fillings.

Quantum criticality in disordered bosonic optical lattices

Using the exact Bose-Fermi mapping, we study universal properties of ground-state density distributions and finite-temperature quantum critical behavior of one-dimensional hard-core bosons in trapped incommensurate optical lattices. Through the analysis of universal scaling relations in the quantum critical regime, we demonstrate that the superfluid to Bose glass transition and the general phase diagram of disordered hard-core bosons can be uniquely determined from finite-temperature density distributions of the trapped disordered system.

A disordered insulator in an optical lattice

Disorder can profoundly affect the transport properties of a wide range of quantum materials. At present, significant disagreement exists regarding features of the disordered Bose–Hubbard model, which is used to study disorder in strongly correlated bosonic systems1,2. Here, by measuring transport3 in a disordered optical lattice4, we discover a disorder-induced superfluid-to-insulator transition in this system, in quantitative agreement with a predicted superfluid–Bose-glass transition from recent numerical simulations5. Both the superfluid-to-insulator transition and correlated changes in the atomic quasimomentum distribution—which verify a simple model for the interplay of disorder and interactions in this system—are phenomena new to the unit-filling regime explored in this work. We find that increasing disorder strength generically leads to greater dissipation, excluding predictions of a disorder-induced or ‘re-entrant’ superfluid. Whereas the absence of a re-entrant superfluid may be explained by finite temperature, the measured bounds on entropy strongly constrain theory.

Correlations and superfluidity of a one-dimensional Bose gas in a quasiperiodic potential

We consider the correlations and superfluid properties of a Bose gas in an external potential. Using a Bogoliubov scheme, we obtain expressions for the correlation function and the superfluid density in an arbitrary external potential. These expressions are applied to a one-dimensional system at zero temperature subject to a quasiperiodic modulation. The critical parameters for the Bose glass transition are obtained using two different criteria and the results are compared. The Lifshits glass is seen to be the limiting case for vanishing interactions.

Superfluid to Bose-Glass Transition in a 1D Weakly Interacting Bose Gas

We study the one-dimensional Bose gas in spatially correlated disorder at zero temperature, using an extended density-phase Bogoliubov method. We analyze, in particular, the decay of the one-body density matrix and the behavior of the Bogoliubov excitations across the phase boundary. We observe that the transition to the Bose-glass phase is marked by a power-law divergence of the density of states at low energy. A measure of the localization length displays a power-law energy dependence in both regions, with the exponent equal to -1 at the boundary. We draw the phase diagram of the superfluid-insulator transition in the limit of small interaction strength.

Vortex phase diagram in heavy ion irradiated untwinned YBa 2Cu 3O y single crystals

In order to study the effects of columnar disorder on the vortex phase diagram, we have measured the resistivity ρ( H, T) and magnetization M( H) in heavy ion irradiated untwinned YBa 2Cu 3O y single crystals. With increasing irradiation dose, the first-order vortex lattice melting transition H m( T) is suppressed near the upper and lower critical points. The first-order melting transition completely disappears when the irradiation dose has a value of 0.5 T < B Φ < 1.0 T and the transition becomes the second-order Bose glass transition when B Φ ⩾ 1.0 T. For B Φ = 0.5 T, the first-order melting transition exists in the very narrow field region between 4.5 T and 10 T without any characteristic features such as the order–disorder transition H ∗( T) line in the vortex solid phase.

Vortex phase diagram in untwinned YBa2Cu3Oy with columnar disorder

We have measured resistivity ρ(H, T) and magnetization M(H) up to 15T in heavy ion irradiated untwinned YBa2Cu3Oy single crystals in order to study effects of columnar disorder on the vortex phase diagram. With increasing irradiation dose B, the first-order vortex lattice melting transition Tm(H) is suppressed near the upper and lower critical points. For B = 0.5 T, the first-order transition exists in the very narrow field region between 4.5 T and 10 T without any characteristic features such as the field-driven order-disorder transition H*(T) line in the vortex solid phase. The first-order transition completely disappears and the transition becomes the second-order Bose glass transition when Bϕ ⩾ 1.0 T.

New transition in the vortex liquid state of YBa2Cu3O7−δ

We have carried out angular dependent magneto-transport measurements on optimally doped, untwinned YBa2Cu3O7−δ crystals irradiated with high energy heavy ions to determine the onset of vortex line tension in the vortex liquid state. The dose matching field was controlled and kept at a low level to partially preserve the first order vortex lattice melting transition. A Bose glass transition is observed below the lower critical point which then transforms into a first order phase transition near 4T. We find that the locus of points which indicates the onset of vortex line tension overlaps with the Bose glass transition line at low fields and then deviates at higher fields, indicating a new transition line in the vortex liquid state. This new line in the vortex liquid phase is dose independent and extends beyond the upper critical point.