Publications

Order by: publication date number of citations

• Scaling of the disorder operator at deconfined quantum criticality

  Yan-Cheng Wang, Nvsen Ma, Meng Cheng, Zi Yang Meng

  SciPost Phys. 13, 123 (2022) · published 14 December 2022 | Toggle abstract · pdf

  We study scaling behavior of the disorder parameter, defined as the expectation value of a symmetry transformation applied to a finite region, at the deconfined quantum critical point in (2+1)$d$ in the $J$-$Q_3$ model via large-scale quantum Monte Carlo simulations. We show that the disorder parameter for U(1) spin rotation symmetry exhibits perimeter scaling with a logarithmic correction associated with sharp corners of the region, as generally expected for a conformally-invariant critical point. However, for large rotation angle the universal coefficient of the logarithmic corner correction becomes negative, which is not allowed in any unitary conformal field theory. We also extract the current central charge from the small rotation angle scaling, whose value is much smaller than that of the free theory.

  26 citations

• Efficient flow equations for dissipative systems

  Gary Schmiedinghoff, Götz S. Uhrig

  SciPost Phys. 13, 122 (2022) · published 13 December 2022 | Toggle abstract · pdf

  Open quantum systems provide an essential theoretical basis for the development of novel quantum technologies, since any real quantum system inevitably interacts with its environment. Lindblad master equations capture the effect of Markovian environments. Closed quantum systems can be treated using flow equations with the particle conserving generator. We generalize this generator to non-Hermitian matrices and open quantum systems governed by Lindbladians, comparing our results with recently proposed generators by Rosso et al. (arXiv:2007.12044). In comparison, we find that our advocated generator provides an efficient flow with good accuracy in spite of truncations.

  3 citations

• Optimal control for Hamiltonian parameter estimation in non-commuting and bipartite quantum dynamics

  Shushen Qin, Marcus Cramer, Christiane P. Koch, Alessio Serafini

  SciPost Phys. 13, 121 (2022) · published 8 December 2022 | Toggle abstract · pdf

  The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of optimal control can be used to identify time-dependent pulses applied to the system to achieve higher precision in the estimation of Hamiltonian parameters, especially in the presence of noise. Here, we extend optimally controlled estimation schemes for single qubits to non-commuting dynamics as well as two interacting qubits, demonstrating improvements in terms of maximal precision, time-stability, as well as robustness over uncontrolled protocols.

  4 citations

• A proposal to extract and enhance four-Majorana interactions in hybrid nanowires

  Tasnum Reza, Sergey M. Frolov, David Pekker

  SciPost Phys. 13, 120 (2022) · published 7 December 2022 | Toggle abstract · pdf

  We simulate the smallest building block of the Sachdev-Ye-Kitaev (SYK) model, a system of four interacting Majorana modes. We propose a 1D Kitaev chain that has been split into three segments, i.e., two topological segments separated by a non-topological segment in the middle, hosting four Majorana Zero Modes at the ends of the topological segments. We add a non-local interaction term to this Hamiltonian which produces both bilinear (two-body) interactions and a quartic (four-body) interaction between the Majorana modes. We further tune the parameters in the Hamiltonian to reach the regime with a finite quartic interaction strength and close to zero bilinear interaction strength, as required by the SYK model. To achieve this, we map the Hamiltonian from Majorana basis to a complex fermion basis, and extract the interaction strengths using a method of characterization of low-lying energy levels and then finding the differences in energies between odd and even parity levels. We show that the interaction strengths can be tuned using two methods - (i) an approximate method of tuning overlapping Majorana wave functions (without non-local interactions) to a zero energy point followed by addition of a non-local interaction, and (ii) a direct parameter space optimization method using a genetic algorithm. We propose that this model could be further extended to more Majorana modes, and show a 6-Majorana model as an example. Since eigenspectral characterization of one-dimensional nanowire devices can be done via tunneling spectroscopy in quantum transport measurements, this study could be performed in experiment.

  1 citation

• Seven Études on dynamical Keldysh model

  Dmitri V. Efremov, Mikhail N. Kiselev

  SciPost Phys. Lect. Notes 65 (2022) · published 6 December 2022 | Toggle abstract · pdf

  We present a comprehensive pedagogical discussion of a family of models describing the propagation of a single particle in a multicomponent non-Markovian Gaussian random field. We report some exact results for single-particle Green's functions, self-energy, vertex part and T-matrix. These results are based on a closed form solution of the Dyson equation combined with the Ward identity. Analytical properties of the solution are discussed. Further we describe the combinatorics of the Feynman diagrams for the Green's function and the skeleton diagrams for the self-energy and vertex, using recurrence relations between the Taylor expansion coefficients of the self-energy. Asymptotically exact equations for the number of skeleton diagrams in the limit of large $N$ are derived. Finally, we consider possible realizations of a multicomponent Gaussian random potential in quantum transport via complex quantum dot experiments.

  1 citation

• dS$\boldsymbol{_2}$ as excitation of AdS$\boldsymbol{_2}$

  Florian Ecker, Daniel Grumiller, Robert McNees

  SciPost Phys. 13, 119 (2022) · published 5 December 2022 | Toggle abstract · pdf

  We introduce a family of 2D dilaton gravity models with state-dependent constant curvature so that dS$_2$ emerges as an excitation of AdS$_2$. Curiously, the strong coupling region corresponds to the asymptotic region geometrically. Apart from these key differences, many features resemble the Almheiri--Polchinski model. We discuss perturbative and non-perturbative thermodynamical stability, bubble nucleation through matter shockwaves, and semiclassical backreaction effects. In some of these models, we find that low temperatures are dominated by AdS$_2$ but high temperatures are dominated by dS$_2$, concurrent with a recent proposal by Susskind.

  6 citations

• Generative learning for the problem of critical slowing down in lattice Gross-Neveu model

  Ankur Singha, Dipankar Chakrabarti, Vipul Arora

  SciPost Phys. Core 5, 052 (2022) · published 2 December 2022 | Toggle abstract · pdf

  In lattice field theory, Monte Carlo simulation algorithms get highly affected by critical slowing down in the critical region, where autocorrelation time increases rapidly. Hence the cost of generation of lattice configurations near the critical region increases sharply. In this paper, we use a Conditional Generative Adversarial Network (C-GAN) for sampling lattice configurations. We train the C-GAN on the dataset consisting of Hybrid Monte Carlo (HMC) samples in regions away from the critical region, i.e., in the regions where the HMC simulation cost is not so high. Then we use the trained C-GAN model to generate independent samples in the critical region. We perform both interpolation and extrapolation to the critical region. Thus, the overall computational cost is reduced. We test our approach for Gross-Neveu model in 1+1 dimension. We find that the observable distributions obtained from the proposed C-GAN model match with those obtained from HMC simulations, while circumventing the problem of critical slowing down.

  4 citations

• The spectral form factor in the 't Hooft limit – Intermediacy versus universality

  Ward L. Vleeshouwers, Vladimir Gritsev

  SciPost Phys. Core 5, 051 (2022) · published 1 December 2022 | Toggle abstract · pdf

  The Spectral Form Factor (SFF) is a convenient tool for the characterization of eigenvalue statistics of systems with discrete spectra, and thus serves as a proxy for quantum chaoticity. This work presents an analytical calculation of the SFF of the Chern-Simons Matrix Model (CSMM), which was first introduced to describe the intermediate level statistics of disordered electrons at the mobility edge. The CSMM is characterized by a parameter $ 0 \leq q\leq 1$, where the Circular Unitary Ensemble (CUE) is recovered for $q\to 0$. The CSMM was later found as a matrix model description of $U(N)$ Chern-Simons theory on $S^3$, which is dual to a topological string theory characterized by string coupling $g_s=-\log q$. The spectral form factor is proportional to a colored HOMFLY invariant of a $(2n,2)$-torus link with its two components carrying the fundamental and antifundamental representations, respectively. We check that taking $N \to \infty$ whilst keeping $q<1$ reduces the connected SFF to an exact linear ramp of unit slope, confirming the main result from arXiv:2012.11703 for the specific case of the CSMM. We then consider the `t Hooft limit, where $N \to \infty$ and $q \to 1^-$ such that $y = q^N $ remains finite. As we take $q\to 1^-$, this constitutes the opposite extreme of the CUE limit. In the `t Hooft limit, the connected SFF turns into a remarkable sequence of polynomials which, as far as the authors are aware, have not appeared in the literature thus far. A gap opens in the spectrum and, after unfolding by a constant rescaling, the connected SFF approximates a linear ramp of unit slope for all $y$ except $y \approx 1$, where the connected SFF goes to zero. We thus find that, although the CSMM was introduced to describe intermediate statistics and the `t Hooft limit is the opposite limit of the CUE, we still recover Wigner-Dyson universality for all $y$ except $y\approx 1$.

  3 citations

• Codebase release 1.0 for Worm Algorithm for Bose-Hubbard and XXZ Models

  Nicolas Sadoune, Lode Pollet

  SciPost Phys. Codebases 9-r1.0 (2022) · published 29 November 2022 | Toggle abstract · src

  We present a novel and open-source implementation of the worm algorithm, which is an algorithm to simulate Bose-Hubbard and sign-positive spin models using a path-integral representation of the partition function. The code can deal with arbitrary lattice structures and assumes spin-exchange terms, or bosonic hopping amplitudes, between nearest-neighbor sites, and local or nearest-neighbor interactions of the density-density type. We explicitly demonstrate the near-linear scaling of the algorithm with respect to the system volume and the inverse temperature and analyze the autocorrelation times in the vicinity of a $U(1)$ second order phase transition. The code is written in such a way that extensions to other lattice models as well as closely-related sign-positive models can be done straightforwardly on top of the provided framework.

  1 citation

• Efficient and scalable path integral Monte Carlo simulations with worm-type updates for Bose-Hubbard and XXZ models

  Nicolas Sadoune, Lode Pollet

  SciPost Phys. Codebases 9 (2022) · published 29 November 2022 | Toggle abstract · pdf

  We present a novel and open-source implementation of the worm algorithm, which is an algorithm to simulate Bose-Hubbard and sign-positive spin models using a path-integral representation of the partition function. The code can deal with arbitrary lattice structures and assumes spin-exchange terms, or bosonic hopping amplitudes, between nearest-neighbor sites, and local or nearest-neighbor interactions of the density-density type. We explicitly demonstrate the near-linear scaling of the algorithm with respect to the system volume and the inverse temperature and analyze the autocorrelation times in the vicinity of a $U(1)$ second order phase transition. The code is written in such a way that extensions to other lattice models as well as closely-related sign-positive models can be done straightforwardly on top of the provided framework.

  7 citations