arXiv subjects

Martin Puschmann

Publications and source records attributed to Martin Puschmann.

11 recordsLinked to original sources

arXiv2024

Critical Behavior and Collective Modes at the Superfluid Transition in Amorphous Systems

We investigate the critical behavior and the dynamics of the amplitude (Higgs) mode close to the superfluid-insulator quantum phase transition in an amorphous system (i.e., a system subject to topological randomness). In particular, we map the two-dimensional Bose-Hubbard Hamiltonian defined on a random Voronoi-Delaunay lattice onto a (2+1)-dimensional layered classical XY model with correlated topological disorder. We study the resulting model by laying recourse to classical Monte Carlo simulations. We specifically focus on the scalar susceptibility of the order parameter to study the dynamics of the amplitude mode. To do so, we harness the maximum entropy method to perform the analytic continuation of the scalar susceptibility to real frequencies. Our analysis shows that the amplitude mode remains delocalized in the presence of such topological disorder, quite at odds with its behavior in generic disordered systems, where the randomness localizes the Higgs mode. Furthermore, we show that the critical behavior of the topologically disordered system is identical to that of its translationally invariant counterpart, consistent with a modified Harris criterion. This suggests that the localization of the collective excitations in the presence of disorder is tied to the critical behavior of the quantum phase transition rather than a simple Anderson-localization-type interference mechanism.

cond-mat.dis-nn↗

arXiv2021

Quartic multifractality and finite-size corrections at the spin quantum Hall transition

The spin quantum Hall (or class C) transition represents one of the few localization-delocalization transitions for which some of the critical exponents are known exactly. Not known, however, is the multifractal spectrum, $\tau_q$, which describes the system-size scaling of inverse participation ratios $P_q$, i.e., the $q$-moments of critical wavefunction amplitudes. We here report simulations based on the class C Chalker-Coddington network and demonstrate that $\tau_q$ is (essentially) a quartic polynomial in $q$. Analytical results fix all prefactors except the quartic curvature that we obtain as $\gamma=(2.22\pm{0.15})\cdot10^{-3}$. In order to achieve the necessary accuracy in the presence of sizable corrections to scaling, we have analyzed the evolution with system size of the entire $P_q$-distribution function. As it turns out, in a sizable window of $q$-values this distribution function exhibits a (single-parameter) scaling collapse already in the pre-asymptotic regime, where finite-size corrections are not negligible. This observation motivates us to propose a novel approach for extracting $\tau_q$ based on concepts borrowed from the Kolmogorov-Smirnov test of mathematical statistics. We believe that our work provides the conceptual means for high-precision investigations of multifractal spectra also near other localization-delocalization transitions of current interest, especially the integer (class A) quantum Hall effect.

cond-mat.dis-nn↗

arXiv2021

Green's functions on a renormalized lattice: An improved method for the integer quantum Hall transition

We introduce a performance-optimized method to simulate localization problems on bipartite tight-binding lattices. It combines an exact renormalization group step to reduce the sparseness of the original problem with the recursive Green's function method. We apply this framework to investigate the critical behavior of the integer quantum Hall transition of a tight-binding Hamiltonian defined on a simple square lattice. In addition, we employ an improved scaling analysis that includes two irrelevant exponents to characterize the shift of the critical energy as well as the corrections to the dimensionless Lyapunov exponent. We compare our findings with the results of a conventional implementation of the recursive Green's function method, and we put them into broader perspective in view of recent development in this field.

cond-mat.dis-nn↗

arXiv2021

Inhomogeneous mean-field approach to collective excitations in disordered interacting bosons

We develop an inhomogeneous quantum mean-field approach to the behavior of collective excitations across the superfluid-Mott glass quantum phase transition in two dimensions, complementing recent quantum Monte Carlo simulations [Phys. Rev. Lett. {\bf 125}, 027002 (2020)]. In quadratic (Gaussian) approximation, the Goldstone (phase) and Higgs (amplitude) modes completely decouple. Each is described by a disordered Bogoliubov Hamiltonian which can be solved by an inhomogeneous multi-mode Bogoliubov transformation. We find that the Higgs mode is spatially localized in both phases. The corresponding scalar spectral function shows a broad peak that is noncritical in the sense that its peak frequency does not soften but remains nonzero across the quantum phase transition. In contrast, the lowest-energy Goldstone mode delocalizes in the superfluid phase, leading to a zero-frequency spectral peak. We compare these findings to the results of the quantum Monte Carlo simulations. We also relate them to general results on the localization of bosonic excitations, and we discuss the limits and generality of our approach.

cond-mat.str-el↗

arXiv2020

Edge state critical behavior of the integer quantum Hall transition

The integer quantum Hall effect features a paradigmatic quantum phase transition. Despite decades of work, experimental, numerical, and analytical studies have yet to agree on a unified understanding of the critical behavior. Based on a numerical Green function approach, we consider the quantum Hall transition in a microscopic model of non-interacting disordered electrons on a simple square lattice. In a strip geometry, topologically induced edge states extend along the system rim and undergo localization-delocalization transitions as function of energy. We investigate the boundary critical behavior in the lowest Landau band and compare it with a recent tight-binding approach to the bulk critical behavior [Phys. Rev. B 99, 121301(R) (2019)] as well as other recent studies of the quantum Hall transition with both open and periodic boundary conditions.

cond-mat.dis-nn↗

arXiv2019

Collective modes at a disordered quantum phase transition

We study the collective excitations, i.e., the Goldstone (phase) mode and the Higgs (amplitude) mode, near the superfluid--Mott glass quantum phase transition in a two-dimensional system of disordered bosons. Using Monte Carlo simulations as well as an inhomogeneous quantum mean-field theory with Gaussian fluctuations, we show that the Higgs mode is strongly localized for all energies, leading to a noncritical scalar response. In contrast, the lowest-energy Goldstone mode undergoes a striking delocalization transition as the system enters the superfluid phase. We discuss the generality of these findings and experimental consequences, and we point out potential relations to many-body localization.

cond-mat.dis-nn↗

arXiv2018

Integer quantum Hall transition on a tight-binding lattice

Even though the integer quantum Hall transition has been investigated for nearly four decades its critical behavior remains a puzzle. The best theoretical and experimental results for the localization length exponent $\nu$ differ significantly from each other, casting doubt on our fundamental understanding. While this discrepancy is often attributed to long-range Coulomb interactions, Gruzberg et al. [Phys. Rev. B 95, 125414 (2017)] recently suggested that the semiclassical Chalker-Coddington model, widely employed in numerical simulations, is incomplete, questioning the established central theoretical results. To shed light on the controversy, we perform a high-accuracy study of the integer quantum Hall transition for a microscopic model of disordered electrons. We find a localization length exponent $\nu=2.58(3)$ validating the result of the Chalker-Coddington network.

cond-mat.dis-nn↗

arXiv2016

Superfluid-Mott glass quantum multicritical point on a percolating lattice

We employ large-scale Monte Carlo simulations to study a particle-hole symmetric site-diluted quantum rotor model in two dimensions. The ground state phase diagram of this system features two distinct quantum phase transitions between the superfluid and the insulating (Mott glass) phases. They are separated by a multicritical point. The generic transition for dilutions below the lattice percolation threshold is driven by quantum fluctuations while the transition across the percolation threshold is due to the geometric fluctuations of the lattice. We determine the location of the multicritical point between these two transitions and find its critical behavior. The multicritical exponents read $z=1.72(2)$, $\beta/\nu=0.41(2)$, and $\gamma/\nu=2.90(5)$ . We compare our results to other quantum phase transitions in disordered systems, and we discuss experiments.

cond-mat.quant-gas↗

arXiv2016

Quantum critical behavior of the superfluid-Mott glass transition

We investigate the zero-temperature superfluid to insulator transitions in a diluted two-dimensional quantum rotor model with particle-hole symmetry. We map the Hamiltonian onto a classical $(2+1)$-dimensional XY model with columnar disorder which we analyze by means of large-scale Monte Carlo simulations. For dilutions below the lattice percolation threshold, the system undergoes a generic superfluid-Mott glass transition. In contrast to other quantum phase transitions in disordered systems, its critical behavior is of conventional power-law type with universal (dilution-independent) critical exponents $z=1.52(3)$, $\nu=1.16(5)$, $\beta/\nu= 0.48(2)$, $\gamma/\nu=2.52(4)$, and $\eta=-0.52(4)$. These values agree with and improve upon earlier Monte-Carlo results [Phys. Rev. Lett. 92, 015703 (2004)] while (partially) excluding other findings in the literature. As a further test of universality, we also consider a soft-spin version of the classical Hamiltonian. In addition, we study the percolation quantum phase transition across the lattice percolation threshold; its critical behavior is governed by the lattice percolation exponents in agreement with recent theoretical predictions. We relate our results to a general classification of phase transitions in disordered systems, and we briefly discuss experiments.

cond-mat.quant-gas↗

arXiv2015

Multifractal analysis of electronic states on random Voronoi-Delaunay lattices

We consider the transport of non-interacting electrons on two- and three-dimensional random Voronoi-Delaunay lattices. It was recently shown that these topologically disordered lattices feature strong disorder anticorrelations between the coordination numbers that qualitatively change the properties of continuous and first-order phase transitions. To determine whether or not these unusual features also influence Anderson localization, we study the electronic wave functions by multifractal analysis and finite-size scaling. We observe only localized states for all energies in the two-dimensional system. In three dimensions, we find two Anderson transitions between localized and extended states very close to the band edges. The critical exponent of the localization length is about 1.6. All these results agree with the usual orthogonal universality class. Additional generic energetic randomness introduced via random potentials does not lead to qualitative changes but allows us to obtain a phase diagram by varying the strength of these potentials.

cond-mat.dis-nn↗

arXiv2015

Analysis of localization-delocalization transitions in corner-sharing tetrahedral lattices

We study the critical behavior of the Anderson localization-delocalization transition in corner-sharing tetrahedral lattices. We compare our results obtained by three different numerical methods namely the multifractal analysis, the Green resolvent method, and the energy-level statistics which yield the singularity strength, the decay length of the wave functions, and the (integrated) energy-level distribution, respectively. From these measures a finite-size scaling approach allows us to determine the critical parameters simultaneously. With particular emphasis we calculate the propagation of the statistical errors by a Monte-Carlo method. We find a high agreement between the results of all methods and we can estimate the highest critical disorder $W_\mathrm{c}=14.474(8)$ at energy $E_\mathrm{c}=-4.0$ and the critical exponent $\nu=1.565(11)$. Our results agree with a previous study by Fazileh et al. but improve accuracy significantly.

cond-mat.dis-nn↗