Publications

Order by: publication date number of citations

• Emergent XY* transition driven by symmetry fractionalization and anyon condensation

  Michael Schuler, Louis-Paul Henry, Yuan-Ming Lu, Andreas M. Läuchli

  SciPost Phys. 14, 001 (2023) · published 11 January 2023 | Toggle abstract · pdf

  Anyons in a topologically ordered phase can carry fractional quantum numbers with respect to the symmetry group of the considered system, one example being the fractional charge of the quasiparticles and quasiholes in the fractional quantum Hall effect. When such symmetry-fractionalized anyons condense, the resulting phase must spontaneously break the symmetry and display a local order parameter. In this paper, we study the phase diagram and anyon condensation transitions of a $\mathbb{Z}_2$ topological order perturbed by Ising interactions in the Toric Code. The interplay between the global (``onsite'') Ising ($\mathbb{Z}_2$) symmetry and the lattice space group symmetries results in a non-trivial symmetry fractionalization class for the anyons, and is shown to lead to two characteristically different confined, symmetry-broken phases. To understand the anyon condensation transitions, we use the recently introduced critical torus energy spectrum technique to identify a line of emergent 2+1D XY* transitions ending at a fine-tuned (Ising$^2$)* critical point. We provide numerical evidence for the occurrence of two symmetry breaking patterns predicted by the specific symmetry fractionalization class of the condensed anyons in the explored phase diagram. In combination with large-scale quantum Monte Carlo simulations we measure unusually large critical exponents $\eta$ for the scaling of the correlation function at the continuous anyon condensation transitions, and we further identify lines of (weakly) first order transitions in the phase diagram. As an important additional result, we discuss the phase diagram of a resulting 2+1D Ashkin-Teller model, where we demonstrate that torus spectroscopy is capable of identifying emergent XY/O(2) critical behaviour, thereby solving some longstanding open questions in the domain of the 3D Ashkin-Teller models. To establish the generality of our results, we propose a field theoretical description capturing the transition from a $\mathbb{Z}_2$ topological order to either $\mathbb{Z}_2$ symmetry broken phase, which is in excellent agreement with the numerical results.

  2 citations

• Co-scattering in micrOMEGAs: A case study for the singlet-triplet dark matter model

  Gaël Alguero, Geneviève Bélanger, Sabine Kraml, Alexander Pukhov

  SciPost Phys. 13, 124 (2022) · published 21 December 2022 | Toggle abstract · pdf

  In scenarios with very small dark matter (DM) couplings and small mass splittings between the DM and other dark sector particles, so-called "co-scattering" or "conversion-driven freeze-out" can be the dominant mechanism for DM production. We present the inclusion of this mechanism in micrOMEGAs together with a case study of the phenomenological implications in the fermionic singlet-triplet model. For the latter, we focus on the transition between co-annihilation and co-scattering processes. We observe that co-scattering is needed to describe the thermal behaviour of the DM for very small couplings, opening up a new region in the parameter space of the model. The triplet states are often long-lived in this region; we therefore also discuss LHC constraints from long-lived signatures obtained with SModelS.

  7 citations

• Topological defects in a double-mirror quadrupole insulator displace diverging charge

  Isidora Araya Day, Anton R. Akhmerov, Dániel Varjas

  SciPost Phys. Core 5, 053 (2022) · published 15 December 2022 | Toggle abstract · pdf

  We show that topological defects in quadrupole insulators do not host quantized fractional charges, contrary to what their Wannier representation indicates. In particular, we test the charge quantization hypothesis based on the Wannier representation of a disclination and a parametric defect. Since disclinations necessarily strain the lattice and parametric defects require closed curves in parameter space, both defects break four-fold rotation symmetry, even away from their origin. The Wannier representation of the defects is thus determined by local reflection symmetries. Contrary to the hypothesis, we find that the local charge density decays as $\sim 1/r^2$ with distance, leading to a diverging defect charge. Because topological defects are incompatible with four-fold rotation symmetry, we conclude that defect charge quantization is protected by sublattice symmetry, and not higher order topology.

  1 citation

• 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.

  22 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.

  2 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.

  5 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