Publications

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Matrix method and the suppression of Runge's phenomenon

Shui-Fa Shen, Wei-Liang Qian, Jie Zhang, Yu Pan, Yu-Peng Yan, Cheng-Gang Shao

SciPost Phys. Core 7, 034 (2024) · published 5 June 2024 | · pdf

Higher-degree polynomial interpolations carried out on uniformly distributed nodes are often plagued by overfitting, known as Runge's phenomenon. This work investigates Runge's phenomenon and its suppression in various versions of the matrix method for black hole quasinormal modes. It is shown that an appropriate choice of boundary conditions gives rise to desirable suppression of oscillations associated with the increasing Lebesgue constant. For the case of discontinuous effective potentials, where the application of the above boundary condition is not feasible, the recently proposed scheme with delimited expansion domain also leads to satisfactory results. The onset of Runge's phenomenon and its effective suppression are demonstrated by evaluating the relevant waveforms. Furthermore, we argue that both scenarios are either closely related to or practical imitations of the Chebyshev grid. The implications of the present study are also addressed.
Quasi-characters in $\widehat{su(2)}$ current algebra at fractional levels

Sachin Grover

SciPost Phys. Core 6, 068 (2023) · published 18 October 2023 | · pdf

We study the even characters of $\widehat{su(2)}$ conformal field theories (CFTs) at admissible fractional levels obtained from the difference of the highest weight characters in the unflavoured limit. We show that admissible even character vectors arise only in three special classes of admissible fractional levels which include the threshold levels, the positive half-odd integer levels, and the isolated level at -$5/4$. Among them, we show that the even characters of the half-odd integer levels map to the difference of characters of $\widehat{su(2)}_{4N+4}$, with $N\in\mathbb{Z}_{>0}$, although we prove that they do not correspond to rational CFTs. The isolated level characters maps to characters of two subsectors with $\widehat{so(5)}_1$ and $\widehat{su(2)}_1$ current algebras. Furthermore, for the $\widehat{su(2)}_1$ subsector of the isolated level, we introduce discrete flavour fugacities. The threshold levels saturate the admissibility bound and their even characters have previously been shown to be proportional to the unflavoured characters of integrable representations in $\widehat{su(2)}_{4N}$ CFTs, where $N\in\mathbb{Z}_{> 0}$ and we reaffirm this result. Except at the three classes of fractional levels, we find special inadmissible characters called quasi-characters which are nice vector valued modular functions but with $q$-series coefficients violating positivity but not integrality.
CDMFT+HFD: An extension of dynamical mean field theory for nonlocal interactions applied to the single band extended Hubbard model

Sarbajaya Kundu, David Sénéchal

SciPost Phys. Core 7, 033 (2024) · published 3 June 2024 | · pdf

We examine the phase diagram of the extended Hubbard model on a square lattice, for both attractive and repulsive nearest-neighbor interactions, using CDMFT+HFD, a combination of Cluster Dynamical Mean Field theory (CDMFT) and a Hartree-Fock mean-field decoupling of the inter-cluster extended interaction. For attractive non-local interactions, this model exhibits a region of phase separation near half-filling, in the vicinity of which we find islands of d-wave superconductivity, decaying rapidly as a function of doping, with disconnected regions of extended s-wave order at smaller (higher) electron densities. On the other hand, when the extended interaction is repulsive, a Mott insulating state at half-filling is destabilized by hole doping, in the strong-coupling limit, in favor of d-wave superconductivity. At the particle-hole invariant chemical potential, we find a first-order phase transition from antiferromagnetism (AF) to d-wave superconductivity as a function of the attractive nearest-neighbor interaction, along with a deviation of the density from the half-filled limit. A repulsive extended interaction instead favors charge-density wave (CDW) order at half-filling.
Interpolating between the gauge and Schrödinger pictures of quantum dynamics

Sayak Guha Roy, Kevin Slagle

SciPost Phys. Core 6, 081 (2023) · published 24 November 2023 | · pdf

Although spatial locality is explicit in the Heisenberg picture of quantum dynamics, spatial locality is not explicit in the Schrödinger picture equations of motion. The gauge picture is a modification of Schrödinger's picture such that locality is explicit in the equations of motion. In order to achieve this explicit locality, the gauge picture utilizes (1) a distinct wavefunction associated with each patch of space, and (2) time-dependent unitary connections to relate the Hilbert spaces associated with nearby patches. In this work, we show that by adding an additional spatially-local term to the gauge picture equations of motion, we can effectively interpolate between the gauge and Schrödinger pictures, such that when this additional term has a large coefficient, all of the gauge picture wavefunctions approach the Schrödginer picture wavefunction (and the connections approach the identity).
Entanglement negativity and defect extremal surface

Yilu Shao, Ma-Ke Yuan, Yang Zhou

SciPost Phys. Core 7, 027 (2024) · published 8 May 2024 | · pdf

We study entanglement negativity for evaporating black hole based on the holographic model with defect brane. We introduce a defect extremal surface formula for entanglement negativity. Based on partial reduction, we show the equivalence between defect extremal surface formula and island formula for entanglement negativity in AdS$_3$/BCFT$_2$. Extending the study to the model of eternal black hole plus CFT bath, we find that black hole-black hole negativity decreases until vanishing, left black hole-left radiation negativity is always a constant, radiation-radiation negativity increases and then saturates at a time later than Page time. In all the time dependent cases, defect extremal surface formula agrees with island formula.
Out of equilibrium many-body expansion dynamics of strongly interacting bosons

Rhombik Roy, Barnali Chakrabarti, Arnaldo Gammal

SciPost Phys. Core 6, 073 (2023) · published 3 November 2023 | · pdf

We solve the Schrödinger equation from first principles to investigate the many-body effects in the expansion dynamics of one-dimensional repulsively interacting bosons released from a harmonic trap. We utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) to solve the many-body Schrödinger equation at high level of accuracy. The MCTDHB basis sets are explicitly time-dependent and optimised by variational principle. We probe the expansion dynamics by three key measures; time evolution of one-, two- and three-body densities. We observe when the mean-field theory results to unimodal expansion, the many-body calculation exhibits trimodal expansion dynamics. The many-body features how the initially fragmented bosons independently spreads out with time whereas the mean-field pictures the expansion of the whole cloud. We also present the three different time scale of dynamics of the inner core, outer core and the cloud as a whole. We analyze the key role played by the dynamical fragmentation during expansion. A Strong evidence of the many-body effects is presented in the dynamics of two- and three-body densities which exhibit correlation hole and pronounced delocalization effect.
Polynomial computational complexity of matrix elements of finite-rank-generated single-particle operators in products of finite bosonic states

Dmitri A. Ivanov

SciPost Phys. Core 7, 022 (2024) · published 22 April 2024 | · pdf

It is known that computing the permanent of the matrix 1+A, where A is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I extend this result to a generalization of the matrix permanent: An expectation value in a product of a large number of identical bosonic states with a bounded number of bosons. This result complements earlier studies on the computational complexity in boson sampling and related setups. The proposed technique based on the Gaussian averaging is equally applicable to bosonic and fermionic systems. This also allows us to improve an earlier polynomial complexity estimate for the fermionic version of the same problem.
Trapping effects in quantum atomic arrays

Pengfei Zhang

SciPost Phys. Core 5, 010 (2022) · published 7 March 2022 | · pdf

Quantum emitters, particularly atomic arrays with subwavelength lattice constant, have been proposed to be an ideal platform for studying the interplay between photons and electric dipoles. In this work, motivated by the recent experiment [1], we develop a microscopic quantum treatment using annihilation and creation operator of atoms in deep optical lattices. Using a diagrammatic approach on the Keldysh contour, we derive the cooperative scattering of the light and obtain the general formula for the $S$ matrix. We apply our method to study the trapping effect, which is beyond previous treatment with spin operators. If the optical lattices are formed by light fields with magical wavelength, the result matches previous results using spin operators. When there is a mismatch between the trapping potentials for atoms in the ground state and the excited state, atomic mirrors become imperfect, with multiple resonances in the optical response. We further study the effect of recoil for large but finite trapping frequency. Our results are consistent with existing experiments.
Stochastic series expansion quantum Monte Carlo for Rydberg arrays

Ejaaz Merali, Isaac J. S. De Vlugt, Roger G. Melko

SciPost Phys. Core 7, 016 (2024) · published 5 April 2024 | · pdf

Arrays of Rydberg atoms are a powerful platform to realize strongly-interacting quantum many-body systems. A common Rydberg Hamiltonian is free of the sign problem, meaning that its equilibrium properties are amenable to efficient simulation by quantum Monte Carlo (QMC). In this paper, we develop a Stochastic Series Expansion QMC algorithm for Rydberg atoms interacting on arbitrary lattices. We describe a cluster update that allows for the efficient sampling and calculation of physical observables for typical experimental parameters, and show that the algorithm can reproduce experimental results on large Rydberg arrays in one and two dimensions.
Topological-insulator nanocylinders

Michele Governale, Fabio Taddei

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

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