Publications

Order by: publication date number of citations

• 3D Ising CFT and exact diagonalization on icosahedron: The power of conformal perturbation theory

  Bing-Xin Lao, Slava Rychkov

  SciPost Phys. 15, 243 (2023) · published 18 December 2023 | Toggle abstract · pdf

  We consider the transverse field Ising model in (2+1)D, putting 12 spins at the vertices of the regular icosahedron. The model is tiny by the exact diagonalization standards, and breaks rotation invariance. Yet we show that it allows a meaningful comparison to the 3D Ising CFT on $\mathbb{R}× S^2$, by including effective perturbations of the CFT Hamiltonian with a handful of local operators. This extreme example shows the power of conformal perturbation theory in understanding finite N effects in models on regularized $S^2$. Its ideal arena of application should be the recently proposed models of fuzzy sphere regularization.

  1 citation

• Reconstructing the potential configuration in a high-mobility semiconductor heterostructure with scanning gate microscopy

  Gaëtan J. Percebois, Antonio Lacerda-Santos, Boris Brun, Benoit Hackens, Xavier Waintal, Dietmar Weinmann

  SciPost Phys. 15, 242 (2023) · published 15 December 2023 | Toggle abstract · pdf

  The weak disorder potential seen by the electrons of a two-dimensional electron gas in high-mobility semiconductor heterostructures leads to fluctuations in the physical properties and can be an issue for nanodevices. In this paper, we show that a scanning gate microscopy (SGM) image contains information about the disorder potential, and that a machine learning approach based on SGM data can be used to determine the disorder. We reconstruct the electric potential of a sample from its experimental SGM data and validate the result through an estimate of its accuracy.

  1 citation

• Identifying Chern numbers of superconductors from local measurements

  Paul Baireuther, Marcin Płodzień, Teemu Ojanen, Jakub Tworzydło, Timo Hyart

  SciPost Phys. Core 6, 087 (2023) · published 15 December 2023 | Toggle abstract · pdf

  Fascination in topological materials originates from their remarkable response properties and exotic quasiparticles which can be utilized in quantum technologies. In particular, large-scale efforts are currently focused on realizing topological superconductors and their Majorana excitations. However, determining the topological nature of superconductors with current experimental probes is an outstanding challenge. This shortcoming has become increasingly pressing due to rapidly developing designer platforms which are theorized to display very rich topology and are better accessed by local probes rather than transport experiments. We introduce a robust machine learning protocol for classifying the topological states of two-dimensional (2D) chiral superconductors and insulators from local density of states (LDOS) data. Since the LDOS can be measured with standard experimental techniques, our protocol contributes to overcoming the almost three decades standing problem of identifying the topological phase of 2D superconductors with broken time-reversal symmetry.

• Superfluid response of two-dimensional filamentary superconductors

  Giulia Venditti, Ilaria Maccari, Alexis Jouan, Gyanendra Singh, Ramesh C. Budhani, Cheryl Feuillet-Palma, Jérôme Lesueur, Nicolas Bergeal, Sergio Caprara, Marco Grilli

  SciPost Phys. 15, 239 (2023) · published 14 December 2023 | Toggle abstract · pdf

  Different classes of low-dimensional superconducting systems exhibit an inhomogeneous filamentary superconducting condensate whose macroscopic coherence still needs to be fully investigated and understood. Here, we present a thorough analysis of the superfluid response of a prototypical filamentary superconductor embedded in a two-dimensional metallic matrix. By mapping the system into an exactly solvable random impedance network, we show how the dissipative (reactive) response of the system non-trivially depends on both the macroscopic and microscopic characteristics of the metallic (superconducting) fraction. We compare our calculations with resonant microwave transport measurements performed on LaAlO$_3$/SrTiO$_3$ heterostructures over an extended range of temperatures and carrier densities finding that the filamentary character of superconductivity accounts for unusual peculiar features of the experimental data.

• Non-parametric learning critical behavior in Ising partition functions: PCA entropy and intrinsic dimension

  Rajat K. Panda, Roberto Verdel, Alex Rodriguez, Hanlin Sun, Ginestra Bianconi, Marcello Dalmonte

  SciPost Phys. Core 6, 086 (2023) · published 14 December 2023 | Toggle abstract · pdf

  We provide and critically analyze a framework to learn critical behavior in classical partition functions through the application of non-parametric methods to data sets of thermal configurations. We illustrate our approach in phase transitions in 2D and 3D Ising models. First, we extend previous studies on the intrinsic dimension of 2D partition function data sets, by exploring the effect of volume in 3D Ising data. We find that as opposed to 2D systems for which this quantity has been successfully used in unsupervised characterizations of critical phenomena, in the 3D case its estimation is far more challenging. To circumvent this limitation, we then use the principal component analysis (PCA) entropy, a "Shannon entropy" of the normalized spectrum of the covariance matrix. We find a striking qualitative similarity to the thermodynamic entropy, which the PCA entropy approaches asymptotically. The latter allows us to extract-through a conventional finite-size scaling analysis with modest lattice sizes-the critical temperature with less than 1% error for both 2D and 3D models while being computationally efficient. The PCA entropy can readily be applied to characterize correlations and critical phenomena in a huge variety of many-body problems and suggests a (direct) link between easy-to-compute quantities and entropies.

  1 citation

• Transient superconductivity in three-dimensional Hubbard systems by combining matrix-product states and self-consistent mean-field theory

  Svenja Marten, Gunnar Bollmark, Thomas Köhler, Salvatore R. Manmana, Adrian Kantian

  SciPost Phys. 15, 236 (2023) · published 12 December 2023 | Toggle abstract · pdf

  We combine matrix-product-state (MPS) and mean-field (MF) methods to model the real-time evolution of a three-dimensional (3D) extended Hubbard system formed from one-dimensional (1D) chains arrayed in parallel with weak coupling in-between them. This approach allows us to treat much larger 3D systems of correlated fermions out-of-equilibrium over a much more extended real-time domain than previous numerical approaches. We deploy this technique to study the evolution of the system as its parameters are tuned from a charge-density wave phase into the superconducting regime, which allows us to investigate the formation of transient non-equilibrium superconductivity. In our ansatz, we use MPS solutions for chains as input for a self-consistent time-dependent MF scheme. In this way, the 3D problem is mapped onto an effective 1D Hamiltonian that allows us to use the MPS efficiently to perform the time evolution, and to measure the BCS order parameter as a function of time. Our results confirm previous findings for purely 1D systems that for such a scenario a transient superconducting state can occur.

• Multipole groups and fracton phenomena on arbitrary crystalline lattices

  Daniel Bulmash, Oliver Hart, Rahul Nandkishore

  SciPost Phys. 15, 235 (2023) · published 12 December 2023 | Toggle abstract · pdf

  Multipole symmetries are of interest in multiple contexts, from the study of fracton phases, to nonergodic quantum dynamics, to the exploration of new hydrodynamic universality classes. However, prior explorations have focused on continuum systems or hypercubic lattices. In this work, we systematically explore multipole symmetries on arbitrary crystal lattices. We explain how, given a crystal structure (specified by a space group and the occupied Wyckoff positions), one may systematically construct all consistent multipole groups. We focus on two-dimensional crystal structures for simplicity, although our methods are general and extend straightforwardly to three dimensions. We classify the possible multipole groups on all two-dimensional Bravais lattices, and on the Kagome and breathing Kagome crystal structures to illustrate the procedure on general crystal lattices. Using Wyckoff positions, we provide an in-principle classification of all possible multipole groups in any space group. We explain how, given a valid multipole group, one may construct a consistent lattice Hamiltonian and a low-energy field theory. We then explore the physical consequences, beginning by generalizing certain results originally obtained on hypercubic lattices to arbitrary crystal structures. Next, we identify two apparently novel phenomena: an emergent, robust subsystem symmetry on the triangular lattice, and an exact multipolar symmetry on the breathing Kagome lattice that does not include conservation of charge (monopole), but instead conserves a vector charge. This makes clear that there is new physics to be found by exploring the consequences of multipolar symmetries on arbitrary lattices, and this work provides the map for the exploration thereof, as well as guiding the search for emergent multipolar symmetries and the attendant exotic phenomena in real materials based on nonhypercubic lattices.

  4 citations

• Boundary states of three dimensional topological order and the deconfined quantum critical point

  Wenjie Ji, Nathanan Tantivasadakarn, Cenke Xu

  SciPost Phys. 15, 231 (2023) · published 7 December 2023 | Toggle abstract · pdf

  We study the boundary states of the archetypal three dimensional topological order, i.e. the three dimensional $\mathbb{Z}_2$ toric code. There are three distinct elementary types of boundary states that we will consider in this work. In the phase diagram that includes the three elementary boundaries there may exist a multi-critical point, which is captured by the so-called deconfined quantum critical point (DQCP) with an "easy-axis" anisotropy. Moreover, there is an emergent $\mathbb{Z}_{2,d}$ symmetry that swaps two of the boundary types, and it becomes part of the global symmetry of the DQCP. The emergent $\mathbb{Z}_{2,d}$ (where d represents "defect") symmetry on the boundary is originated from a type of surface defect in the bulk. We further find a gapped boundary with a surface topological order that is invariant under the emergent symmetry.

  2 citations

• Phenomenological XXZ model for the competition between superconductivity and charge order in cuprates

  Giulia Venditti, Ilaria Maccari, Jose Lorenzana, Sergio Caprara

  SciPost Phys. 15, 230 (2023) · published 7 December 2023 | Toggle abstract · pdf

  We argue that there is a special doping point in the phase diagram of cuprates, such that the condensation of holes into a charge-ordered and a superconducting phase are degenerate in energy but with an energy barrier in between. We present Monte Carlo simulations of a phenomenological XXZ model for this problem without and with quenched disorder in two dimensions. While in the clean case charge order and superconductivity are separated by a first-order line which is nearly independent of temperature, in the presence of quenched disorder charge order is fragmented into domains separated by superconducting filaments reminiscent of the supersolid behaviour in $^4$He. Assuming weak interlayer couplings, the resulting phase diagram of the three-dimensional system is in good agreement with the experiments.

  1 citation

• Spin rotons and supersolids in binary antidipolar condensates

  Wyatt Kirkby, Thomas Bland, Francesca Ferlaino, Russell N. Bisset

  SciPost Phys. Core 6, 084 (2023) · published 4 December 2023 | Toggle abstract · pdf

  We present a theoretical study of a mixture of antidipolar and nondipolar Bose-Einstein condensates confined to an infinite tube. We predict the presence of a spin roton and its associated instability, which triggers a continuous unmodulated-to-supersolid phase transition. We characterize the phase diagram of the binary system, ranging from the quasi-1D to the radial Thomas-Fermi (elongated 3D) regimes. We also present the dynamic formation of supersolids following a quench from the uniform miscible phase, which maintains phase coherence across the system.

  1 citation