Publications

Order by: publication date number of citations

• Temperature dependence of quasiparticle interference in $d$-wave superconductors

  Harun Al Rashid, Garima Goyal, Alireza Akbari, Dheeraj Kumar Singh

  SciPost Phys. Core 6, 033 (2023) · published 24 April 2023 | Toggle abstract · pdf

  We investigate the temperature dependence of quasiparticle interference in the high $T_c$-cuprates using an exact-diagonalization + Monte-Carlo based scheme to simulate the $d$-wave superconducting order parameter. The quasiparticle interference patterns have features largely resulting from the scattering vectors of the octet model at lower temperature. Our findings suggest that the features of quasiparticle interference in the pseudogap region of the phase diagram are also dominated by the set of scattering vectors belonging to the octet model because of the persisting antinodal gap beyond the superconducting transition $T_c$. However, beyond a temperature when the antinodal gap becomes very small, a set of scattering vectors different from those belonging to the octet model are responsible for the quasiparticle interference patterns. With a rise in temperature, the patterns are increasingly broadened.

  5 citations

• Topological-insulator nanocylinders

  Michele Governale, Fabio Taddei

  SciPost Phys. Core 6, 032 (2023) · published 21 April 2023 | Toggle abstract · pdf

  Nanostructures, such a quantum dots or nanoparticles, made of three-dimensional topological insulators (3DTIs) have been recently attracting increasing interest, especially for their optical properties. In this paper we calculate the energy spectrum, the surface states and the dipole matrix elements for optical transitions with in-plane polarization of 3DTI nanocylinders of finite height $L$ and radius $R$. We first derive an effective 2D Hamiltonian by exploiting the cylindrical symmetry of the problem. We develop two approaches: the first one is an exact numerical tight-binding model obtained by discretising the Hamiltonian. The second one, which allows us to obtain analytical results, is an approximated model based on a large-$R$ expansion and on an effective boundary condition to account for the finite height of the nanocylinder. We find that the agreement between the two models, as far as eigenenergies and eigenfunctions are concerned, is excellent for the lowest absolute value of the longitudinal component of the angular momentum. Finally, we derive analytical expressions for the dipole matrix elements by first considering the lateral surface alone and the bases alone, and then for the whole nanocylinder. In particular, we focus on the two limiting cases of tall and squat nanocylinders. The latter case is compared with the numerical results finding a good agreement.

• Majorana bound states in encapsulated bilayer graphene

  Fernando Peñaranda, Ramón Aguado, Elsa Prada, Pablo San-Jose

  SciPost Phys. 14, 075 (2023) · published 18 April 2023 | Toggle abstract · pdf

  The search for robust topological superconductivity and Majorana bound states continues, exploring both one-dimensional (1D) systems such as semiconducting nanowires and two-dimensional (2D) platforms. In this work we study a 2D approach based on graphene bilayers encapsulated in transition metal dichalcogenides that, unlike previous proposals involving the Quantum Hall regime in graphene, requires weaker magnetic fields and does not rely on interactions. The encapsulation induces strong spin-orbit coupling on the graphene bilayer, which opens a sizeable gap and stabilizes fragile pairs of helical edge states. We show that, when subject to an in-plane Zeeman field, armchair edges can be transformed into p-wave one-dimensional topological superconductors by contacting them laterally with conventional superconductors. We demonstrate the emergence of Majorana bound states (MBSs) at the sample corners of crystallographically perfect flakes, belonging either to the D or the BDI symmetry classes depending on parameters. We compute the phase diagram, the resilience of MBSs against imperfections, and their manifestation as a 4$\pi$-periodic effect in Josephson junction geometries, all suggesting the existence of a topological phase within experimental reach.

  9 citations

• Optimal compression of quantum many-body time evolution operators into brickwall circuits

  Maurits S. J. Tepaske, Dominik Hahn, David J. Luitz

  SciPost Phys. 14, 073 (2023) · published 17 April 2023 | Toggle abstract · pdf

  Near term quantum computers suffer from a degree of decoherence which is prohibitive for high fidelity simulations with deep circuits. An economical use of circuit depth is therefore paramount. For digital quantum simulation of quantum many-body systems, real time evolution is typically achieved by a Trotter decomposition of the time evolution operator into circuits consisting only of two qubit gates. To match the geometry of the physical system and the CNOT connectivity of the quantum processor, additional SWAP gates are needed. We show that optimal fidelity, beyond what is achievable by simple Trotter decompositions for a fixed gate count, can be obtained by compiling the evolution operator into optimal brickwall circuits for the $S=1/2$ quantum Heisenberg model on chains and ladders, when mapped to one dimensional quantum processors without the need of additional SWAP gates.

  24 citations

• Finite-time bounds on the probabilistic violation of the second law of thermodynamics

  Harry J. D. Miller, Martí Perarnau-Llobet

  SciPost Phys. 14, 072 (2023) · published 17 April 2023 | Toggle abstract · pdf

  Jarzynski's equality sets a strong bound on the probability of violating the second law of thermodynamics by extracting work beyond the free energy difference. We derive finite-time refinements to this bound for driven systems in contact with a thermal Markovian environment, which can be expressed in terms of the geometric notion of thermodynamic length. We show that finite-time protocols converge to Jarzynski's bound at a rate slower than $1/\sqrt{\tau}$, where $\tau$ is the total time of the work-extraction protocol. Our result highlights a new application of minimal dissipation processes and demonstrates a connection between thermodynamic geometry and the higher order statistical properties of work.

  4 citations

• Extracting electronic many-body correlations from local measurements with artificial neural networks

  Faluke Aikebaier, Teemu Ojanen, Jose L. Lado

  SciPost Phys. Core 6, 030 (2023) · published 17 April 2023 | Toggle abstract · pdf

  The characterization of many-body correlations provides a powerful tool for analyzing correlated quantum materials. However, experimental extraction of quantum entanglement in correlated electronic systems remains an open problem in practice. In particular, the correlation entropy quantifies the strength of quantum correlations in interacting electronic systems, yet it requires measuring all the single-particle correlators of a macroscopic sample. To circumvent this bottleneck, we introduce a strategy to obtain the correlation entropy of electronic systems solely from a set of local measurements. We show that, by combining local particle-particle and density-density correlations with a neural-network algorithm, the correlation entropy can be predicted accurately. Specifically, we show that for a generalized interacting fermionic model, our algorithm yields an accurate prediction of the correlation entropy from a set of noisy local correlators. Our work shows that the correlation entropy in interacting electron systems can be reconstructed from local measurements, providing a starting point to experimentally extract many-body correlations with local probes.

  11 citations

• Bootstrapping traceless symmetric $O(N)$ scalars

  Marten Reehorst, Maria Refinetti, Alessandro Vichi

  SciPost Phys. 14, 068 (2023) · published 12 April 2023 | Toggle abstract · pdf

  We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors of $O(N)$ with two indices $t_{ij}$. We obtain upper bounds on operator dimensions for all the relevant representations and several values of $N$. We discover several families of kinks, which do not correspond to any known model and we discuss possible candidates. We then specialize to the case $N=4$, which has been conjectured to describe a phase transition in the antiferromagnetic real projective model $ARP^{3}$. Lattice simulations provide strong evidence for the existence of a second order phase transition, while an effective field theory approach does not predict any fixed point. We identify a set of assumptions that constrain operator dimensions to a closed region overlapping with the lattice prediction. The region is still present after pushing the numerics in the single correlator case or when considering a mixed system involving $t$ and the lowest dimension scalar singlet.

  9 citations

• Topological insulators and geometry of vector bundles

  Alexander S. Sergeev

  SciPost Phys. Lect. Notes 67 (2023) · published 12 April 2023 | Toggle abstract · pdf

  For a long time, band theory of solids has focused on the energy spectrum, or Hamiltonian eigenvalues. Recently, it was realized that the collection of eigenvectors also contains important physical information. The local geometry of eigenspaces determines the electric polarization, while their global twisting gives rise to the metallic surface states in topological insulators. These phenomena are central topics of the present notes. The shape of eigenspaces is also responsible for many intriguing physical analogies, which have their roots in the theory of vector bundles. We give an informal introduction to the geometry and topology of vector bundles and describe various physical models from this mathematical perspective.

  1 citation

• Codimension-2 defects and higher symmetries in (3+1)D topological phases

  Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang, Ryohei Kobayashi, Nathanan Tantivasadakarn, Guanyu Zhu

  SciPost Phys. 14, 065 (2023) · published 11 April 2023 | Toggle abstract · pdf

  (3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error-correcting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension-2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of $\mathbb{Z}_2$ gauge theory with fermionic charges, in $\mathbb{Z}_2 \times \mathbb{Z}_2$ gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral ($D_n$) and alternating ($A_6$) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an $H^4$ cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. The equations involving background gauge fields for the 3-group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with non-Abelian flux loops (defining part of a non-invertible higher symmetry), examples of non-invertible codimension-2 defects, and examples of the interplay of codimension-2 defects with codimension-1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D $A_6$ gauge theory.

  27 citations

• Photoemission "experiments" on holographic lattices

  Filip Herček, Vladan Gecin, Mihailo Čubrović

  SciPost Phys. Core 6, 027 (2023) · published 6 April 2023 | Toggle abstract · pdf

  We construct a 2D holographic ionic lattice with hyperscaling-violating infrared geometry and study single-electron spectral functions ("ARPES photoemission curves") on this background. The spectra typically show a three-peak structure, where the central peak undergoes a crossover from a sharp but not Fermi-liquid-like quasiparticle to a wide incoherent maximum, and the broad side peaks resemble the Hubbard bands. These findings are partially explained by a perturbative near-horizon analysis of the bulk Dirac equation. Comparing the holographic Green functions in imaginary frequency with the Green functions of the Hubbard model obtained from quantum Monte Carlo, we find that the holographic model provides a very good fit to the Hubbard Green function. However, the information loss when transposing the holographic Green functions to imaginary frequencies implies that a deeper connection to Hubbard-like models remains questionable.

  3 citations