Publications

Order by: publication date number of citations

• $m^*$ of two-dimensional electron gas: A neural canonical transformation study

  Hao Xie, Linfeng Zhang, Lei Wang

  SciPost Phys. 14, 154 (2023) · published 14 June 2023 | Toggle abstract · pdf

  The quasiparticle effective mass $m^\ast$ of interacting electrons is a fundamental quantity in the Fermi liquid theory. However, the precise value of the effective mass of uniform electron gas is still elusive after decades of research. The newly developed neural canonical transformation approach [Xie et al., J. Mach. Learn. 1, (2022)] offers a principled way to extract the effective mass of electron gas by directly calculating the thermal entropy at low temperature. The approach models a variational many-electron density matrix using two generative neural networks: an autoregressive model for momentum occupation and a normalizing flow for electron coordinates. Our calculation reveals a suppression of effective mass in the two-dimensional spin-polarized electron gas, which is more pronounced than previous reports in the low-density strong-coupling region. This prediction calls for verification in two-dimensional electron gas experiments.

  4 citations

• Topological and quantum critical properties of the interacting Majorana chain model

  Natalia Chepiga, Nicolas Laflorencie

  SciPost Phys. 14, 152 (2023) · published 13 June 2023 | Toggle abstract · pdf

  We study Majorana chain with the shortest possible interaction term and in the presence of hopping alternation. When formulated in terms of spins the model corresponds to the transverse field Ising model with nearest-neighbor transverse and next-nearest-neighbor longitudinal repulsion. The phase diagram obtained with extensive DMRG simulations is very rich and contains six phases. Four gapped phases include paramagnetic, period-2 with broken translation symmetry, $\mathbb{Z}_2$ with broken parity symmetry and the period-2-$\mathbb{Z}_2$ phase with both symmetries broken. In addition there are two floating phases: gapless and critical Luttinger liquid with incommensurate correlations, and with an additional spontaneously broken $\mathbb{Z}_2$ symmetry in one of them. By analyzing an extended phase diagram we demonstrate that, in contrast with a common belief, the Luttinger liquid phase along the self-dual critical line terminates at a weaker interaction strength than the end point of the Ising critical line that we find to be in the tri-critical Ising universality class. We also show that none of these two points is a Lifshitz point terminating the incommensurability. In addition, we analyzed topological properties through Majorana zero modes emergent in the two topological phases, with and without incommensurability. In the weak interaction regime, a self-consistent mean-field treatment provides a remarkable accuracy for the description of the spectral pairing and the parity switches induced by the interaction.

  3 citations

• Parametrization and thermodynamic scaling of pair correlation functions for the fractional quantum Hall effect

  Jørgen Fulsebakke, Mikael Fremling, Niall Moran, Joost K. Slingerland

  SciPost Phys. 14, 149 (2023) · published 9 June 2023 | Toggle abstract · pdf

  The calculation of pair correlations and density profiles of quasiholes are routine steps in the study of proposed fractional quantum Hall states. Nevertheless, the field has not adopted a standard way to present the results of such calculations in an easily reproducible form. We develop a polynomial expansion that allows for easy quantitative comparison between different candidate wavefunctions, as well as reliable scaling of correlation and quasihole profiles to the thermodynamic limit. We start from the well-known expansion introduced by Girvin [PRB, 30 (1984)] (see also [Girvin, MacDonald and Platzman, PRB, 33 (1986)]), which is physically appealing but, as we demonstrate, numerically unstable. We orthogonalize their basis set to obtain a new basis of modified Jacobi polynomials, whose coefficients can be stably calculated. We then apply our expansion to extract pair correlation expansion coefficients and quasihole profiles in the thermodynamic limit for a wide range of fractional quantum Hall wavefunctions. These include the Laughlin series, composite fermion states with both reverse and direct flux attachment, the Moore-Read Pfaffian state, and BS hierarchy states. The expansion procedure works for both abelian and non-abelian quasiholes, even when the density at the core is not zero. We find that the expansion coefficients for all quantum Hall states considered can be fit remarkably well using a cosine oscillation with exponentially decaying amplitude. The frequency and the decay length are related in an intuitive, but not elementary way to the filling fraction. Different states at the same filling fraction can have distinct values for these parameters. Finally, we also use our scaled correlation functions to calculate estimates for the magneto-roton gaps of the various states.

• Competition between frustration and spin dimensionality in the classical antiferromagnetic $n$-vector model with arbitrary $n$

  Nikolaos P. Konstantinidis

  SciPost Phys. Core 6, 042 (2023) · published 8 June 2023 | Toggle abstract · pdf

  A new method to characterize the strength of magnetic frustration is proposed by calculating the minimum dimensionality of the absolute ground states of the classical nearest-neighbor antiferromagnetic $n$-vector model with arbitrary $n$. Platonic solids in three and four dimensions and Archimedean solids have lowest-energy configurations in a number of spin dimensions equal to their real-space dimensionality. Fullerene molecules and geodesic icosahedra can produce ground states in as many as five spin dimensions. Frustration is also characterized by the maximum value of the round-state energy when the exchange interactions are allowed to vary.

  2 citations

• Strong Hilbert space fragmentation via emergent quantum drums in two dimensions

  Anwesha Chattopadhyay, Bhaskar Mukherjee, Krishnendu Sengupta, Arnab Sen

  SciPost Phys. 14, 146 (2023) · published 7 June 2023 | Toggle abstract · pdf

  We introduce a disorder-free model of $S=1/2$ spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment. We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space. Given any product state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as "quantum drums". These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum. The spectra of some small drums is calculated analytically. We study two bigger quasi-one-dimensional drums numerically, dubbed "wire" and a "junction of two wires" respectively. We find that these possess a chaotic spectrum but also support distinct families of quantum many-body scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the one-dimensional PXP chain with open boundaries, a paradigmatic model for quantum many-body scarring; while the junction of two wires represents a distinct constrained model.

  5 citations

• Arrested development and fragmentation in strongly-interacting Floquet systems

  Matthew Wampler, Israel Klich

  SciPost Phys. 14, 145 (2023) · published 7 June 2023 | Toggle abstract · pdf

  We explore how interactions can facilitate classical like dynamics in models with sequentially activated hopping. Specifically, we add local and short range interaction terms to the Hamiltonian and ask for conditions ensuring the evolution acts as a permutation on initial local number Fock states. We show that at certain values of hopping and interactions, determined by a set of Diophantine equations, such evolution can be realized. When only a subset of the Diophantine equations is satisfied the Hilbert space can be fragmented into frozen states, states obeying cellular automata like evolution, and subspaces where evolution mixes Fock states and is associated with eigenstates exhibiting high entanglement entropy and level repulsion.

  2 citations

• Field-induced local Fermi-liquid states in the underscreened Kondo model for Eu compounds

  Shingo Kuniyoshi, Ryousuke Shiina

  SciPost Phys. Proc. 11, 015 (2023) · published 6 June 2023 | Toggle abstract · pdf

  We have studied an underscreened Kondo model for the impurity spin $S=7/2$ capturing the $4f$ characteristics of a nearly divalent Eu ion. By using the numerical renormalization group method, it is shown that an unusual heavy-fermion state is induced from the underscreened spin state when a weak crystal field is introduced. It is also found that the application of the magnetic field enhances the effective mass of the heavy fermions, reflecting the field-induced level crossing of the spin states. We will discuss the mechanism of these mass enhancements in terms of a realization of the two-stage Kondo effect.

• Josephson effects between the Kitaev ladder superconductors

  Osamu Kanehira, Hiroki Tsuchiura

  SciPost Phys. Proc. 11, 014 (2023) · published 6 June 2023 | Toggle abstract · pdf

  The two-leg ladder system consisting of the Kitaev chains is known to exhibit a richer phase diagram than that of the single chain. We theoretically investigate the variety of the Josephson effects between the ladder systems. We consider the Josephson phase difference $\theta$ between these two ladder systems as well as the phase difference $\phi$ between the parallel chains in each ladder system. The total energy of the junction at $T = 0$ is calculated by a numerical diagonalization method as functions of $\theta$, $\phi$, and also a transverse hopping $t_{\perp}$ in the ladders. We find that, by controlling $t_{\perp}$ and $\phi$, the junction exhibits not only the fractional Josephson effect for the phase difference $\theta$, but also the usual 0-junction and even $\pi$-junction properties.

• Hidden-orders of uranium compounds

  Hisatomo Harima

  SciPost Phys. Proc. 11, 006 (2023) · published 5 June 2023 | Toggle abstract · pdf

  Hidden order is often discussed in strongly correlated electron systems. In many cases, it shows no magnetic responses, so that the order parameter is electric, but accompanies few lattice distortion. In the Jahn-Teller cases, the ordered state gains its energy by changing inter-site mixing strengths, leading a larger structural distortion with lowering symmetry. On the contrary, in strongly correlated electron systems, the strong intra-site Coulomb energy causes the the symmetry lowering. It is not necessary to bring the lattice distortion for lowering local site symmetry. In fact, lower symmetry of electronic state than the symmetry of the crystal structure can be found for UTe$_2$, UGe$_2$ similarly for URu$_2$Si$_2$.

  1 citation

• A testable theory for high-Tc superconductivity in cuprates

  Eduardo C. Marino

  SciPost Phys. Proc. 11, 004 (2023) · published 5 June 2023 | Toggle abstract · pdf

  A number of theories for the superconductivity in cuprates, have been proposed in the more than 30 years that have elapsed since its discovery. A common feature of these theories is the small number, or even the absence, of quantitative predictions that could be compared to a vast number of experimental data, which are, conversely, available. Such theories are, consequently non-testable. We describe the foundations and a number of applications of a theory describing High-Tc Superconductivity in cuprates, which we proposed recently, that besides being testable, has proven to meet successfully the tests to which it has been submitted so far.