Publications

Order by: publication date number of citations

• Monopole harmonics on $\mathbb{CP}^{n-1}$

  Dmitri Bykov, Andrei Smilga

  SciPost Phys. 15, 195 (2023) · published 14 November 2023 | Toggle abstract · pdf

  We find the spectra and eigenfunctions of both ordinary and supersymmetric quantum-mechanical models describing the motion of a charged particle over the $\mathbb{CP}^{n-1}$ manifold in the presence of a background monopole-like gauge field. The states form degenerate $SU(n)$ multiplets and their wave functions acquire a very simple form being expressed via homogeneous coordinates. Their relationship to multidimensional orthogonal polynomials of a special kind is discussed. By the well-known isomorphism between the twisted Dolbeault and Dirac complexes, our construction also gives the eigenfunctions and eigenvalues of the Dirac operator on complex projective spaces in a monopole background.

  2 citations

• Probing fractional statistics in quantum simulators of spin liquid Hamiltonians

  Shiyu Zhou, Maria Zelenayova, Oliver Hart, Claudio Chamon, Claudio Castelnovo

  SciPost Phys. 15, 194 (2023) · published 14 November 2023 | Toggle abstract · pdf

  Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases in a noisy quantum environment. One of the most promising tools is investigating the behaviour of the topological excitations, and in particular their fractional statistics. In this work we put forward a generic route to achieve this, and we illustrate it in the specific case of $\mathbb{Z}_2$ topological spin liquids implemented with the aid of combinatorial gauge symmetry. We design a convenient architecture to study signatures of fractional statistics via quasiparticle interferometry, and we assess its robustness to diagonal and off-diagonal disorder, as well as to dephasing - effects that are generally pervasive in current quantum programmable devices. Interestingly, when turned on its head, our scheme provides a remarkably clear test of the "quantumness" of these devices, with robust signatures that crucially hinge on quantum coherence and quantum interference effects, and cannot be mimicked by classical stochastic processes.

  2 citations

• Average symmetry protected higher-order topological amorphous insulators

  Yu-Liang Tao, Jiong-Hao Wang, Yong Xu

  SciPost Phys. 15, 193 (2023) · published 14 November 2023 | Toggle abstract · pdf

  While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline counterparts. Here we theoretically demonstrate the existence of higher-order topological insulators in two-dimensional amorphous systems that can host more than six corner modes, such as eight or twelve corner modes. Although individual sample configuration lacks crystalline symmetry, we find that an ensemble of all configurations exhibits an average crystalline symmetry that provides protection for the new topological phases. To characterize the topological phases, we construct two topological invariants. Even though the bulk energy gap in the topological phase vanishes in the thermodynamic limit, we show that the bulk states near zero energy are localized, as supported by the level-spacing statistics and inverse participation ratio. Our findings open an avenue for exploring average symmetry protected higher-order topological phases in amorphous systems without crystalline counterparts.

  9 citations

• Quasi-particle functional renormalisation group calculations in the two-dimensional t-t'-Hubbard model

  Daniel Rohe

  SciPost Phys. 15, 192 (2023) · published 13 November 2023 | Toggle abstract · pdf

  We extend and apply a recently introduced quasi-particle functional renormalisation group scheme to the two-dimensional Hubbard model with next-nearest-neighbour hopping and away from half filling. We confirm the generation of superconducting correlations in some regions of the phase diagram, but also find that the inclusion of self-energy feedback by means of a decreasing quasi-particle weight can suppress superconducting tendencies more than anti-ferromagnetic correlations by which they are generated. As a supplement, we provide sample results for the self-energy in second-order perturbation theory and address some conceptual matters.

  1 citation

• Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain

  He-Ran Wang, Bo Li, Fei Song, Zhong Wang

  SciPost Phys. 15, 191 (2023) · published 13 November 2023 | Toggle abstract · pdf

  We study the open XXZ spin chain with a $PT$-symmetric non-Hermitian boundary field. We find an interaction-induced scale-free non-Hermitian skin effect by using the coordinate Bethe Ansatz. The steady-state and the ground state in the $PT$ broken phase are constructed, and the formulas of their eigen-energies in the thermodynamic limit are obtained. The differences between the many-body scale-free states and the boundary string states are explored, and the transition between the two at the isotropic point is investigated. We also discuss an experimental scheme to verify our results.

  7 citations

• Probing chaos in the spherical p-spin glass model

  Lorenzo Correale, Anatoli Polkovnikov, Marco Schirò, Alessandro Silva

  SciPost Phys. 15, 190 (2023) · published 13 November 2023 | Toggle abstract · pdf

  We study the dynamics of a quantum $p$-spin glass model starting from initial states defined in microcanonical shells, in a classical regime. We compute different chaos estimators, such as the Lyapunov exponent and the Kolmogorov-Sinai entropy, and find a marked maximum as a function of the energy of the initial state. By studying the relaxation dynamics and the properties of the energy landscape we show that the maximal chaos emerges in correspondence with the fastest spin relaxation and the maximum complexity, thus suggesting a qualitative picture where chaos emerges as the trajectories are scattered over the exponentially many saddles of the underlying landscape. We also observe hints of ergodicity breaking at low energies, indicated by the correlation function and a maximum of the fidelity susceptibility.

  2 citations

• Dynamics of parafermionic states in transport measurements

  Ida Egholm Nielsen, Jens Schulenborg, Reinhold Egger, Michele Burrello

  SciPost Phys. 15, 189 (2023) · published 8 November 2023 | Toggle abstract · pdf

  Advances in hybrid fractional quantum Hall (FQH)-superconductor platforms pave the way for realisation of parafermionic modes. We analyse signatures of these non-abelian anyons in transport measurements across devices with $\mathbb{Z}_6$ parafermions (PFs) coupled to an external electrode. Simulating the dynamics of these open systems by a stochastic quantum jump method, we show that a current readout over sufficiently long times constitutes a projective measurement of the fractional charge shared by two PFs. Interaction of these topological modes with the FQH environment, however, may cause poisoning events affecting this degree of freedom which we model by jump operators that describe incoherent coupling of PFs with FQH edge modes. We analyse how this gives rise to a characteristic three-level telegraph noise in the current, constituting a very strong signature of PFs. We discuss also other forms of poisoning and noise caused by interaction with fractional quasiparticles in the bulk of the Hall system. We conclude our work with an analysis of four-PF devices, in particular on how the PF fusion algebra can be observed in electrical transport experiments.

  2 citations

• A quantum register using collective excitations in a Bose-Einstein condensate

  Elisha Haber, Zekai Chen, Nicholas P. Bigelow

  SciPost Phys. 15, 188 (2023) · published 8 November 2023 | Toggle abstract · pdf

  A qubit made up of an ensemble of atoms is attractive due to its resistance to atom losses. In this work, we consider an experimentally feasible protocol to coherently load a spin-dependent optical lattice from a spatially overlapping Bose-Einstein condensate. Identifying each lattice site as a qubit, with an empty or filled site as the qubit basis, we discuss how high-fidelity single-qubit operations, two-qubit gates between arbitrary pairs of qubits, and nondestructive measurements could be performed. In this setup, the effect of atom losses has been mitigated, the atoms never need to be removed from the ground state manifold, and separate storage and computational bases for the qubits are not required, all of which can be significant sources of decoherence in many other types of atomic qubits.

• Massive particle interferometry with lattice solitons

  Piero Naldesi, Juan Polo, Peter D. Drummond, Vanja Dunjko, Luigi Amico, Anna Minguzzi, Maxim Olshanii

  SciPost Phys. 15, 187 (2023) · published 8 November 2023 | Toggle abstract · pdf

  We discuss an interferometric scheme employing interference of bright solitons formed as specific bound states of attracting bosons on a lattice. We revisit the proposal of Castin and Weiss [Phys. Rev. Lett. vol. 102, 010403 (2009)] for using the scattering of a quantum matter-wave soliton on a barrier in order to create a coherent superposition state of the soliton being entirely to the left of the barrier and being entirely to the right of the barrier. In that proposal, it was assumed that the scattering is perfectly elastic, i.e. that the center-of-mass kinetic energy of the soliton is lower than the chemical potential of the soliton. Here we relax this assumption: By employing a combination of Bethe ansatz and DMRG-based analysis of the dynamics of the appropriate many-body system, we find that the interferometric fringes persist even when the center-of-mass kinetic energy of the soliton is above the energy needed for its complete dissociation into constituent atoms.

  2 citations

• Circuit Complexity through phase transitions: Consequences in quantum state preparation

  Sebastián Roca-Jerat, Teresa Sancho-Lorente, Juan Román-Roche, David Zueco

  SciPost Phys. 15, 186 (2023) · published 8 November 2023 | Toggle abstract · pdf

  In this paper, we analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition. We discuss different definitions of complexity, namely the one following the Fubini-Study metric or the Nielsen complexity. We also explore different models: Ising, ZZXZ or Dicke. In addition, different forms of state preparation are investigated: analytic or exact diagonalization techniques, adiabatic algorithms (with and without shortcuts), and Quantum Variational Eigensolvers. We find that the divergence (or lack thereof) of the complexity near a phase transition depends on the non-local character of the operations used to reach the ground state. For Fubini-Study based complexity, we extract the universal properties and their critical exponents. In practical algorithms, we find that the complexity depends crucially on whether or not the system passes close to a quantum critical point when preparing the state. For both VQE and Adiabatic algorithms, we provide explicit expressions and bound the growth of complexity with respect to the system size and the execution time, respectively.

  2 citations