Publications

Order by: publication date number of citations

• Continuously varying critical exponents in long-range quantum spin ladders

  Patrick Adelhardt, Kai Phillip Schmidt

  SciPost Phys. 15, 087 (2023) · published 11 September 2023 | Toggle abstract · pdf

  We investigate the quantum-critical behavior between the rung-singlet phase with hidden string order and the Néel phase with broken SU(2)-symmetry in quantum spin ladders with algebraically decaying unfrustrated long-range Heisenberg interactions. To this end, we determine high-order series expansions of energies and observables in the thermodynamic limit about the isolated rung-dimer limit. This is achieved by extending the method of perturbative continuous unitary transformations (pCUT) to long-range Heisenberg interactions and to the calculation of generic observables. The quantum-critical breakdown of the rung-singlet phase then allows us to determine the critical phase transition line and the entire set of critical exponents as a function of the decay exponent of the long-range interaction. We demonstrate long-range mean-field behavior as well as a non-trivial regime of continuously varying critical exponents implying the absence of deconfined criticality contrary to a recent suggestion in the literature.

  9 citations

• Many versus one: The disorder operator and entanglement entropy in fermionic quantum matter

  Weilun Jiang, Bin-Bin Chen, Zi Hong Liu, Junchen Rong, Fakher F. Assaad, Meng Cheng, Kai Sun, Zi Yang Meng

  SciPost Phys. 15, 082 (2023) · published 7 September 2023 | Toggle abstract · pdf

  Motivated by recent development of the concept of the disorder operator and its relation with entanglement entropy in bosonic systems, here we show the disorder operator successfully probes many aspects of quantum entanglement in fermionic many-body systems. From both analytical and numerical computations in free and interacting fermion systems in 1D and 2D, we find the disorder operator and the entanglement entropy exhibit similar universal scaling behavior, as a function of the boundary length of the subsystem, but with subtle yet important differences. In 1D they both follow the $\log{L}$ scaling behavior with the coefficient determined by the Luttinger parameter for disorder operator, and the conformal central charge for entanglement entropy. In 2D they both show the universal $L\log L$ scaling behavior in free and interacting Fermi liquid states, with the coefficients depending on the geometry of the Fermi surfaces. However at a 2D quantum critical point with non-Fermi-liquid state, extra symmetry information is needed in the design of the disorder operator, so as to reveal the critical fluctuations as does the entanglement entropy. Our results demonstrate the fermion disorder operator can be used to probe quantum many-body entanglement related to global symmetry, and provide new tools to explore the still largely unknown territory of highly entangled fermion quantum matter in 2 or higher dimensions.

  23 citations

• Impurity Knight shift in quantum dot Josephson junctions

  Luka Pavešić, Marta Pita Vidal, Arno Bargerbos, Rok Žitko

  SciPost Phys. 15, 070 (2023) · published 24 August 2023 | Toggle abstract · pdf

  Spectroscopy of a Josephson junction device with an embedded quantum dot reveals the presence of a contribution to level splitting in external magnetic field that is proportional to $\cos\phi$, where $\phi$ is the gauge-invariant phase difference across the junction. To elucidate the origin of this unanticipated effect, we systematically study the Zeeman splitting of spinful subgap states in the superconducting Anderson impurity model. The magnitude of the splitting is renormalized by the exchange interaction between the local moment and the continuum of Bogoliubov quasiparticles in a variant of the Knight shift phenomenon. The leading term in the shift is linear in the hybridisation strength $\Gamma$ (quadratic in electron hopping), while the subleading term is quadratic in $\Gamma$ (quartic in electron hopping) and depends on $\phi$ due to spin-polarization-dependent corrections to the Josephson energy of the device. The amplitude of the $\phi$-dependent part is largest for experimentally relevant parameters beyond the perturbative regime where it is investigated using numerical renormalization group calculations. Such magnetic-field-tunable coupling between the quantum dot spin and the Josephson current could find wide use in superconducting spintronics.

  6 citations

• Automatic, high-order, and adaptive algorithms for Brillouin zone integration

  Jason Kaye, Sophie Beck, Alex Barnett, Lorenzo Van Muñoz, Olivier Parcollet

  SciPost Phys. 15, 062 (2023) · published 15 August 2023 | Toggle abstract · pdf

  We present efficient methods for Brillouin zone integration with a non-zero but possibly very small broadening factor $\eta$, focusing on cases in which downfolded Hamiltonians can be evaluated efficiently using Wannier interpolation. We describe robust, high-order accurate algorithms automating convergence to a user-specified error tolerance $\varepsilon$, emphasizing an efficient computational scaling with respect to $\eta$. After analyzing the standard equispaced integration method, applicable in the case of large broadening, we describe a simple iterated adaptive integration algorithm effective in the small $\eta$ regime. Its computational cost scales as $\mathcal{O}(\log^3(\eta^{-1}))$ as $\eta \to 0^+$ in three dimensions, as opposed to $\mathcal{O}(\eta^{-3})$ for equispaced integration. We argue that, by contrast, tree-based adaptive integration methods scale only as $\mathcal{O}(\log(\eta^{-1})/\eta^{2})$ for typical Brillouin zone integrals. In addition to its favorable scaling, the iterated adaptive algorithm is straightforward to implement, particularly for integration on the irreducible Brillouin zone, for which it avoids the tetrahedral meshes required for tree-based schemes. We illustrate the algorithms by calculating the spectral function of SrVO$_3$ with broadening on the meV scale.

  4 citations

• Diagnosing weakly first-order phase transitions by coupling to order parameters

  Jonathan D'Emidio, Alexander A. Eberharter, Andreas M. Läuchli

  SciPost Phys. 15, 061 (2023) · published 14 August 2023 | Toggle abstract · pdf

  The hunt for exotic quantum phase transitions described by emergent fractionalized degrees of freedom coupled to gauge fields requires a precise determination of the fixed point structure from the field theoretical side, and an extreme sensitivity to weak first-order transitions from the numerical side. Addressing the latter, we revive the classic definition of the order parameter in the limit of a vanishing external field at the transition. We demonstrate that this widely understood, yet so far unused approach provides a diagnostic test for first-order versus continuous behavior that is distinctly more sensitive than current methods. We first apply it to the family of $Q$-state Potts models, where the nature of the transition is continuous for $Q\leq4$ and turns (weakly) first order for $Q>4$, using an infinite system matrix product state implementation. We then employ this new approach to address the unsettled question of deconfined quantum criticality in the $S=1/2$ Néel to valence bond solid transition in two dimensions, focusing on the square lattice $J$-$Q$ model. Our quantum Monte Carlo simulations reveal that both order parameters remain finite at the transition, directly confirming a first-order scenario with wide reaching implications in condensed matter and quantum field theory.

  17 citations

• Weak ergodicity breaking in non-Hermitian many-body systems

  Qianqian Chen, Shuai A. Chen, Zheng Zhu

  SciPost Phys. 15, 052 (2023) · published 7 August 2023 | Toggle abstract · pdf

  The recent discovery of persistent revivals in the Rydberg-atom quantum simulator has revealed a weakly ergodicity-breaking mechanism dubbed quantum many-body scars, which are a set of nonthermal states embedded in otherwise thermal spectra. Until now, such a mechanism has been mainly studied in Hermitian systems. Here, we establish the non-Hermitian quantum many-body scars and systematically characterize their nature from dynamic revivals, entanglement entropy, physical observables, and energy level statistics. Notably, we find the non-Hermitian quantum many-body scars exhibit significantly enhanced coherent revival dynamics when approaching the exceptional point. The signatures of non-Hermitian scars switch from the real-energy axis to the imaginary-energy axis after a real-to-complex spectrum transition driven by increasing non-Hermiticity, where an exceptional point and a quantum tricritical point emerge simultaneously. We further examine the stability of non-Hermitian quantum many-body scars against external fields, reveal the non-Hermitian quantum criticality and eventually set up the whole phase diagram. The possible connection to the open quantum many-body systems is also explored. Our findings offer insights for realizing long-lived coherent states in non-Hermitian many-body systems.

  16 citations

• Quantum chaos in interacting Bose-Bose mixtures

  Tran Duong Anh-Tai, Mathias Mikkelsen, Thomas Busch, Thomás Fogarty

  SciPost Phys. 15, 048 (2023) · published 4 August 2023 | Toggle abstract · pdf

  The appearance of chaotic quantum dynamics significantly depends on the symmetry properties of a system, and in cold atomic systems many of these can be experimentally controlled. In this work, we systematically study the emergence of quantum chaos in a minimal system describing one-dimensional harmonically trapped Bose-Bose mixtures by tuning the particle-particle interactions. Using an improved exact diagonalization scheme, we examine the transition from integrability to chaos when the inter-component interaction changes from weak to strong. Our study is based on the analysis of the level spacing distribution and the distribution of the matrix elements of observables in terms of the eigenstate thermalization hypothesis and their dynamics. We show that one can obtain strong signatures of chaos by increasing the inter-component interaction strength and breaking the symmetry of intra-component interactions.

  6 citations

• Nonequilibrium phases of ultracold bosons with cavity-induced dynamic gauge fields

  Arkadiusz Kosior, Helmut Ritsch, Farokh Mivehvar

  SciPost Phys. 15, 046 (2023) · published 3 August 2023 | Toggle abstract · pdf

  Gauge fields are a central concept in fundamental theories of physics, and responsible for mediating long-range interactions between elementary particles. Recently, it has been proposed that dynamical gauge fields can be naturally engineered by photons in composite, neutral quantum gas-cavity systems using suitable atom-photon interactions. Here we comprehensively investigate nonequilibrium dynamical phases appearing in a two-leg bosonic lattice model with leg-dependent, dynamical complex tunnelings mediated by cavity-assisted two-photon Raman processes. The system constitutes a minimal dynamical flux-lattice model. We study fixed points of the equations of motion and their stability, the resultant dynamical phase diagram, and the corresponding phase transitions and bifurcations. Notably, the phase diagram features a plethora of nonequilibrium dynamical phases including limit-cycle and chaotic phases. In the end, we relate regular periodic dynamics (i.e., limit-cycle phases) of the system to time crystals.

  12 citations

• Universality in Anderson localization on random graphs with varying connectivity

  Piotr Sierant, Maciej Lewenstein, Antonello Scardicchio

  SciPost Phys. 15, 045 (2023) · published 3 August 2023 | Toggle abstract · pdf

  We perform a thorough and complete analysis of the Anderson localization transition on several models of random graphs with regular and random connectivity. The unprecedented precision and abundance of our exact diagonalization data (both spectra and eigenstates), together with new finite size scaling and statistical analysis of the graph ensembles, unveils a universal behavior which is described by two simple, integer, scaling exponents. A by-product of such analysis is a reconciliation of the tension between the results of perturbation theory coming from strong disorder and earlier numerical works, which seemed to suggest that there should be a non-ergodic region above a given value of disorder $W_{E}$ which is strictly less than the Anderson localization critical disorder $W_C$, and that of other works which suggest that there is no such region. We find that, although no separate $W_{E}$ exists from $W_C$, the length scale at which fully developed ergodicity is found diverges like $|W-W_C|^{-1}$, while the critical length over which delocalization develops is $\sim |W-W_C|^{-1/2}$. The separation of these two scales at the critical point allows for a true non-ergodic, delocalized region. In addition, by looking at eigenstates and studying leading and sub-leading terms in system size-dependence of participation entropies, we show that the former contain information about the non-ergodicity volume which becomes non-trivial already deep in the delocalized regime. We also discuss the quantitative similarities between the Anderson transition on random graphs and many-body localization transition.

  31 citations

• The classical Heisenberg model on the centred pyrochlore lattice

  Rajah P. Nutakki, Ludovic D. C. Jaubert, Lode Pollet

  SciPost Phys. 15, 040 (2023) · published 1 August 2023 | Toggle abstract · pdf

  The centred pyrochlore lattice is a novel geometrically frustrated lattice, realized in the metal-organic framework Mn(ta)$_2$ [Phys. Rev. Research 5, L022018 (2023)] where the basic unit of spins is a five site centred tetrahedron. Here, we present an in-depth theoretical study of the $J_1-J_2$ classical Heisenberg model on this lattice, using a combination of mean-field analytical methods and Monte Carlo simulations. We find a rich phase diagram with low temperature states exhibiting ferrimagnetic order, partial ordering, and a highly degenerate spin liquid with distinct regimes of low temperature correlations. We discuss in detail how the regime displaying broadened pinch points in its spin structure factor is consistent with an effective description in terms of a fluid of interacting charges. We also show how this picture holds in two dimensions on the analogous centred kagome lattice and elucidate the connection to the physics of thin films in ($d+1$) dimensions. Furthermore, we show that a Coulomb phase can be stabilized on the centred pyrochlore lattice by the addition of further neighbour couplings. This demonstrates the centred pyrochlore lattice is an experimentally relevant geometry which naturally hosts emergent gauge fields in the presence of charges at low energies.

  4 citations