Publications

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• Comparing many-body approaches against the helium atom exact solution

  Jing Li, N. D. Drummond, Peter Schuck, Valerio Olevano

  SciPost Phys. 6, 040 (2019) · published 1 April 2019 | Toggle abstract · pdf

  Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schr\"odinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the GW approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.

  19 citations

• Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

  Yi-Hsien Du, Umang Mehta, Dung Xuan Nguyen, Dam Thanh Son

  SciPost Phys. 12, 050 (2022) · published 2 February 2022 | Toggle abstract · pdf

  We propose nonabelian higher-rank gauge theories in 2+1D and 3+1D. The gauge group is constructed from the volume-preserving diffeomorphisms of space. We show that the intriguing physics of the lowest Landau level (LLL) limit can be interpreted as the consequences of the symmetry. We derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term within our formalism. Using the gauge symmetry in 2+1D, we derive the LLL effective action of vortex crystal in rotating Bose gas as well as Wigner crystal of electron in an applied magnetic field. We show that the non-linear sigma models of ferromagnet in 2+1D and 3+1D exhibit the higher-rank gauge symmetries that we introduce in this paper. We interpret the fractonic behavior of the excitations on the lowest Landau level and of skyrmions in ferromagnets as the consequence of the higher-rank gauge symmetry.

  19 citations

• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables

  Jean Michel Maillet, Giuliano Niccoli

  SciPost Phys. 6, 071 (2019) · published 21 June 2019 | Toggle abstract · pdf

  We apply our new approach of quantum Separation of Variables (SoV) to the complete characterization of the transfer matrix spectrum of quantum integrable lattice models associated to gl(n)-invariant R-matrices in the fundamental representations. We consider lattices with N sites and quasi-periodic boundary conditions associated to an arbitrary twist K having simple spectrum (but not necessarily diagonalizable). In our approach the SoV basis is constructed in an universal manner starting from the direct use of the conserved charges of the models, i.e., from the commuting family of transfer matrices. Using the integrable structure of the models, incarnated in the hierarchy of transfer matrices fusion relations, we prove that our SoV basis indeed separates the spectrum of the corresponding transfer matrices. Moreover, the combined use of the fusion rules, of the known analytic properties of the transfer matrices and of the SoV basis allows us to obtain the complete characterization of the transfer matrix spectrum and to prove its simplicity. Any transfer matrix eigenvalue is completely characterized as a solution of a so-called quantum spectral curve equation that we obtain as a difference functional equation of order n. Namely, any eigenvalue satisfies this equation and any solution of this equation having prescribed properties leads to an eigenvalue. We construct the associated eigenvector, unique up to normalization, by computing its decomposition on the SoV basis that is of a factorized form written in terms of the powers of the corresponding eigenvalues. If the twist matrix K is diagonalizable with simple spectrum then the transfer matrix is also diagonalizable with simple spectrum. In that case, we give a construction of the Baxter Q-operator satisfying a T-Q equation of order n, the quantum spectral curve equation, involving the hierarchy of the fused transfer matrices.

  19 citations

• Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice

  Shenghan Jiang, Panjin Kim, Jung Hoon Han, Ying Ran

  SciPost Phys. 7, 006 (2019) · published 9 July 2019 | Toggle abstract · pdf

  The properties of ground state of spin-$\frac{1}{2}$ kagome antiferromagnetic Heisenberg (KAFH) model have attracted considerable interest in the past few decades, and recent numerical simulations reported a spin liquid phase. The nature of the spin liquid phase remains unclear. For instance, the interplay between symmetries and $Z_2$ topological order leads to different types of $Z_2$ spin liquid phases. In this paper, we develop a numerical simulation method based on symmetric projected entangled-pair states (PEPS), which is generally applicable to strongly correlated model systems in two spatial dimensions. We then apply this method to study the nature of the ground state of the KAFH model. Our results are consistent with that the ground state is a $U(1)$ Dirac spin liquid rather than a $Z_2$ spin liquid.

  19 citations

• Fermionization and boundary states in 1+1 dimensions

  Yoshiki Fukusumi, Yuji Tachikawa, Yunqin Zheng

  SciPost Phys. 11, 082 (2021) · published 25 October 2021 | Toggle abstract · pdf

  In the last few years it was realized that every fermionic theory in 1+1 dimensions is a generalized Jordan-Wigner transform of a bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry. In this note we determine how the boundary states are mapped under this correspondence. We also interpret this mapping as the fusion of the original boundary with the fermionization interface.

  19 citations

• Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors

  Max Geier, Ion Cosma Fulga, Alexander Lau

  SciPost Phys. 10, 092 (2021) · published 26 April 2021 | Toggle abstract · pdf

  We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct $d$-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to $(d-2)$-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.

  19 citations

• Light-induced topological magnons in two-dimensional van der Waals magnets

  Emil Viñas Boström, Martin Claassen, James W. McIver, Gregor Jotzu, Angel Rubio, Michael A. Sentef

  SciPost Phys. 9, 061 (2020) · published 30 October 2020 | Toggle abstract · pdf

  Driving a two-dimensional Mott insulator with circularly polarized light breaks time-reversal and inversion symmetry, which induces an optically-tunable synthetic scalar spin chirality interaction in the effective low-energy spin Hamiltonian. Here, we show that this mechanism can stabilize topological magnon excitations in honeycomb ferromagnets and in optical lattices. We find that the irradiated quantum magnet is described by a Haldane model for magnons that hosts topologically-protected edge modes. We study the evolution of the magnon spectrum in the Floquet regime and via time propagation of the magnon Hamiltonian for a slowly varying pulse envelope. Compared to similar but conceptually distinct driving schemes based on the Aharanov-Casher effect, the dimensionless light-matter coupling parameter $\lambda = eEa/\hbar\omega$ at fixed electric field strength is enhanced by a factor $\sim 10^5$. This increase of the coupling parameter allows to induce a topological gap of the order of $\Delta \approx 2$ meV with realistic laser pulses, bringing an experimental realization of light-induced topological magnon edge states within reach.

  19 citations

• Fermionic Gaussian states: an introduction to numerical approaches

  Jacopo Surace, Luca Tagliacozzo

  SciPost Phys. Lect. Notes 54 (2022) · published 16 May 2022 | Toggle abstract · pdf

  This document is meant to be a practical introduction to the analytical and numerical manipulation of Fermionic Gaussian systems. Starting from the basics, we move to relevant modern results and techniques, presenting numerical examples and studying relevant Hamiltonians, such as the transverse field Ising Hamiltonian, in detail. We finish introducing novel algorithms connecting Fermionic Guassian states with matrix product states techniques. All the numerical examples make use of the free Julia package F_utilities.

  19 citations

• Gifts from anomalies: Exact results for Landau phase transitions in metals

  Zhengyan Darius Shi, Hart Goldman, Dominic V. Else, T. Senthil

  SciPost Phys. 13, 102 (2022) · published 1 November 2022 | Toggle abstract · pdf

  Non-Fermi liquid phenomena arise naturally near critical points of Landau ordering transitions in metallic systems, where strong fluctuations of a bosonic order parameter destroy coherent quasiparticles. Despite progress in developing controlled perturbative techniques, much of the low energy physics of such metallic quantum critical points remains poorly understood. We demonstrate that exact, non-perburbative results can be obtained for both optical transport and static susceptibilities in "Hertz-Millis" theories of Fermi surfaces coupled to critical bosons. Such models possess a large emergent symmetry and anomaly structure, which we leverage to fix these quantities. In particular, we show that in the infrared limit, the boson self energy at zero wave vector, $\mathbf{q}=0$, is a constant independent of frequency, and the real part of the optical conductivity, $\sigma(\omega)$, is purely a delta function Drude peak with no other corrections. Therefore, further frequency dependence in the boson self energy or optical conductivity can only come from irrelevant operators in a clean system. Exact relations between Fermi liquid parameters as the critical point is approached from the disordered phase are also obtained. The absence of a universal, power law frequency dependence in the boson self energy contrasts with previous perturbative calculations, and we explain the origin of this difference.

  19 citations

• Metallic and insulating stripes and their relation with superconductivity in the doped Hubbard model

  Luca F. Tocchio, Arianna Montorsi, Federico Becca

  SciPost Phys. 7, 021 (2019) · published 12 August 2019 | Toggle abstract · pdf

  The dualism between superconductivity and charge/spin modulations (the so-called stripes) dominates the phase diagram of many strongly-correlated systems. A prominent example is given by the Hubbard model, where these phases compete and possibly coexist in a wide regime of electron dopings for both weak and strong couplings. Here, we investigate this antagonism within a variational approach that is based upon Jastrow-Slater wave functions, including backflow correlations, which can be treated within a quantum Monte Carlo procedure. We focus on clusters having a ladder geometry with $M$ legs (with $M$ ranging from $2$ to $10$) and a relatively large number of rungs, thus allowing us a detailed analysis in terms of the stripe length. We find that stripe order with periodicity $\lambda=8$ in the charge and $2\lambda=16$ in the spin can be stabilized at doping $\delta=1/8$. Here, there are no sizable superconducting correlations and the ground state has an insulating character. A similar situation, with $\lambda=6$, appears at $\delta=1/6$. Instead, for smaller values of dopings, stripes can be still stabilized, but they are weakly metallic at $\delta=1/12$ and metallic with strong superconducting correlations at $\delta=1/10$, as well as for intermediate (incommensurate) dopings. Remarkably, we observe that spin modulation plays a major role in stripe formation, since it is crucial to obtain a stable striped state upon optimization. The relevance of our calculations for previous density-matrix renormalization group results and for the two-dimensional case is also discussed.

  19 citations