Publications

Order by: publication date number of citations

• Multipole groups and fracton phenomena on arbitrary crystalline lattices

  Daniel Bulmash, Oliver Hart, Rahul Nandkishore

  SciPost Phys. 15, 235 (2023) · published 12 December 2023 | Toggle abstract · pdf

  Multipole symmetries are of interest in multiple contexts, from the study of fracton phases, to nonergodic quantum dynamics, to the exploration of new hydrodynamic universality classes. However, prior explorations have focused on continuum systems or hypercubic lattices. In this work, we systematically explore multipole symmetries on arbitrary crystal lattices. We explain how, given a crystal structure (specified by a space group and the occupied Wyckoff positions), one may systematically construct all consistent multipole groups. We focus on two-dimensional crystal structures for simplicity, although our methods are general and extend straightforwardly to three dimensions. We classify the possible multipole groups on all two-dimensional Bravais lattices, and on the Kagome and breathing Kagome crystal structures to illustrate the procedure on general crystal lattices. Using Wyckoff positions, we provide an in-principle classification of all possible multipole groups in any space group. We explain how, given a valid multipole group, one may construct a consistent lattice Hamiltonian and a low-energy field theory. We then explore the physical consequences, beginning by generalizing certain results originally obtained on hypercubic lattices to arbitrary crystal structures. Next, we identify two apparently novel phenomena: an emergent, robust subsystem symmetry on the triangular lattice, and an exact multipolar symmetry on the breathing Kagome lattice that does not include conservation of charge (monopole), but instead conserves a vector charge. This makes clear that there is new physics to be found by exploring the consequences of multipolar symmetries on arbitrary lattices, and this work provides the map for the exploration thereof, as well as guiding the search for emergent multipolar symmetries and the attendant exotic phenomena in real materials based on nonhypercubic lattices.

  4 citations

• Radiation, entanglement and islands from a boundary local quench

  Lorenzo Bianchi, Stefano De Angelis, Marco Meineri

  SciPost Phys. 14, 148 (2023) · published 8 June 2023 | Toggle abstract · pdf

  We study the entanglement and the energy density of the radiation emitted after a local quench in a boundary conformal field theory. We use the operator product expansion (OPE) to predict the early- and late-time behavior of the entanglement entropy and we find, under mild assumptions, a universal form for the leading term, which we test on some treatable two-dimensional examples. We also derive a general upper bound on the entanglement, valid along the full time evolution. In two dimensions, the bound is computed analytically, while in higher dimensions it is evaluated at early and late time via the OPE. These CFT predictions are then compared with a doubly-holographic setup where the CFT is interpreted as a reservoir for the radiation produced on an end-of-the-world brane. After finding the gravitational dual of a boundary local quench, we compute the time evolution of the holographic entanglement entropy, whose late-time behavior is in perfect agreement with the CFT predictions. In the brane+bath picture, unitarity of the time evolution is preserved thanks to the formation of an island. The holographic results can be recovered explicitly from the island formula, in the limit where the tension of the brane is close to the maximal value.

  4 citations

• Engineering spectral properties of non-interacting lattice Hamiltonians

  Ali G. Moghaddam, Dmitry Chernyavsky, Corentin Morice, Jasper van Wezel, Jeroen van den Brink

  SciPost Phys. 11, 109 (2021) · published 22 December 2021 | Toggle abstract · pdf

  We investigate the spectral properties of one-dimensional lattices with position-dependent hopping amplitudes and on-site potentials that are smooth bounded functions of the position. We find an exact integral form for the density of states (DOS) in the limit of an infinite number of sites, which we derive using a mixed Bloch-Wannier basis consisting of piecewise Wannier functions. Next, we provide an exact solution for the inverse problem of constructing the position-dependence of hopping in a lattice model yielding a given DOS. We confirm analytic results by comparing them to numerics obtained by exact diagonalization for various incarnations of position-dependent hoppings and on-site potentials. Finally, we generalize the DOS integral form to multi-orbital tight-binding models with longer-range hoppings and in higher dimensions.

  4 citations

• Building models of topological quantum criticality from pivot Hamiltonians

  Nathanan Tantivasadakarn, Ryan Thorngren, Ashvin Vishwanath, Ruben Verresen

  SciPost Phys. 14, 013 (2023) · published 2 February 2023 | Toggle abstract · pdf

  Progress in understanding symmetry-protected topological (SPT) phases has been greatly aided by our ability to construct lattice models realizing these states. In contrast, a systematic approach to constructing models that realize quantum critical points between SPT phases is lacking, particularly in dimension $d>1$. Here, we show how the recently introduced notion of the pivot Hamiltonian—generating rotations between SPT phases—facilitates such a construction. We demonstrate this approach by constructing a spin model on the triangular lattice, which is midway between a trivial and SPT phase. The pivot Hamiltonian generates a $U(1)$ pivot symmetry which helps to stabilize a direct SPT transition. The sign-problem free nature of the model—with an additional Ising interaction preserving the pivot symmetry—allows us to obtain the phase diagram using quantum Monte Carlo simulations. We find evidence for a direct transition between trivial and SPT phases that is consistent with a deconfined quantum critical point with emergent $SO(5)$ symmetry. The known anomaly of the latter is made possible by the non-local nature of the $U(1)$ pivot symmetry. Interestingly, the pivot Hamiltonian generating this symmetry is nothing other than the staggered Baxter-Wu three-spin interaction. This work illustrates the importance of $U(1)$ pivot symmetries and proposes how to generally construct sign-problem-free lattice models of SPT transitions with such anomalous symmetry groups for other lattices and dimensions.

  4 citations

• Transient Features in Charge Fractionalization, Local Equilibration and Non-equilibrium Bosonization

  Alexander Schneider, Mirco Milletari, Bernd Rosenow

  SciPost Phys. 2, 007 (2017) · published 25 February 2017 | Toggle abstract · pdf

  In quantum Hall edge states and in other one-dimensional interacting systems, charge fractionalization can occur due to the fact that an injected charge pulse decomposes into eigenmodes propagating at different velocities. If the original charge pulse has some spatial width due to injection with a given source-drain voltage, a finite time is needed until the separation between the fractionalized pulses is larger than their width. In the formalism of non-equilibrium bosonization, the above physics is reflected in the separation of initially overlapping square pulses in the effective scattering phase. When expressing the single particle Green's function as a functional determinant of counting operators containing the scattering phase, the time evolution of charge fractionalization is mathematically described by functional determinants with overlapping pulses. We develop a framework for the evaluation of such determinants, describe the system's equilibration dynamics, and compare our theoretical results with recent experimental findings.

  4 citations

• Quantum computation with cat qubits

  Jérémie Guillaud, Joachim Cohen, Mazyar Mirrahimi

  SciPost Phys. Lect. Notes 72 (2023) · published 16 June 2023 | Toggle abstract · pdf

  These are the lecture notes from the 2019 Les Houches Summer School on "Quantum Information Machines". After a brief introduction to quantum error correction and bosonic codes, we focus on the case of cat qubits stabilized by a nonlinear multi-photon driven dissipation process. We argue that such a system can be seen as a self-correcting qubit where bit-flip errors are robustly and exponentially suppressed. Next, we provide some experimental directions to engineer such a multi-photon driven dissipation process with superconducting circuits. Finally, we analyze various logical gates that can be implemented without re-introducing bit-flip errors. This set of bias-preserving gates pave the way towards a hardware-efficient and fault-tolerant quantum processor.

  4 citations

• Optically detected magnetic resonance with an open source platform

  Hossein Babashah, Hoda Shirzad, Elena Losero, Valentin Goblot, Christophe Galland, Mayeul Chipaux

  SciPost Phys. Core 6, 065 (2023) · published 9 October 2023 | Toggle abstract · pdf

  Localized electronic spins in solid-state environments form versatile and robust platforms for quantum sensing, metrology and quantum information processing. With optically detected magnetic resonance (ODMR), it is possible to prepare and readout highly coherent spin systems, up to room temperature, with orders of magnitude enhanced sensitivities and spatial resolutions compared to induction-based techniques, allowing for single spin manipulations. While ODMR was first observed in organic molecules, many other systems have since then been identified. Among them is the nitrogen-vacancy (NV) center in diamond, which is used both as a nanoscale quantum sensor for external fields and as a spin qubit. Other systems permitting ODMR are rare earth ions used as quantum memories and many other color centers trapped in bulk or 2-dimensional host materials. In order to allow the broadest possible community of researchers and engineers to investigate and develop novel ODMR-based materials and applications, we review here the setting up of ODMR experiments using commercially available hardware. We also present in detail the dedicated collaborative open-source interface named Qudi and describe the features we added to speed-up data acquisition, relax instrument requirements and extend its applicability to ensemble measurements. Covering both hardware and software development, this article aims to overview the setting of ODMR experiments and provide an efficient, portable and collaborative interface to implement innovative experiments to optimize the development time of ODMR experiments for scientists of any backgrounds.

  4 citations

• Why space could be quantised on a different scale to matter

  Matthew J. Lake

  SciPost Phys. Proc. 4, 014 (2021) · published 13 August 2021 | Toggle abstract · pdf

  The scale of quantum mechanical effects in matter is set by Planck's constant, $\hbar$. This represents the quantisation scale for material objects. In this article, we present a simple argument why the quantisation scale for space, and hence for gravity, may not be equal to $\hbar$. Indeed, assuming a single quantisation scale for both matter and geometry leads to the `worst prediction in physics', namely, the huge difference between the observed and predicted vacuum energies. Conversely, assuming a different quantum of action for geometry, $\beta \ll \hbar$, allows us to recover the observed density of the Universe. Thus, by measuring its present-day expansion, we may in principle determine, empirically, the scale at which the geometric degrees of freedom should be quantised.

  4 citations

• Non-standard interactions in $\tau^- \to (\pi^-\eta,\pi^-\pi^0)\nu_{\tau}$ decays

  Gabriel López Castro

  SciPost Phys. Proc. 1, 008 (2019) · published 18 February 2019 | Toggle abstract · pdf

  Originally thought as clean processes to study the hadronization of the weak currents, semileptonic tau lepton decays can be useful to set constraints on non-standard (NS) weak interactions. In this talk we summarize our recent studies on the effects of NS interactions in $\tau^- \to (\pi^-\pi^0,\pi^-\eta)\nu_{\tau}$ decays. We find that experimental data on these decays provide strong constraints on NS scalar and tensor interactions, respectively. Further improved measurements at Belle II and a better knowledge of necessary tensor and scalar form factors will allow to set limits on these NS interactions that are similar or better to contraints obtained from other low-energy processes

  4 citations

• Wormholes from averaging over states

  Ben Freivogel, Dora Nikolakopoulou, Antonio F. Rotundo

  SciPost Phys. 14, 026 (2023) · published 1 March 2023 | Toggle abstract · pdf

  An important question about black holes is to what extent a typical pure state differs from the ensemble average. We show that this question can be answered within semi-classical gravity. We focus on the quantum deviation, which measures the fluctuations in the expectation value of an operator in an ensemble of pure states. For a large class of ensembles and observables, these fluctuations are calculated by a correlation function in the eternal black hole background, which can be reliably calculated within semi-classical gravity. This implements the idea of [arXiv:2002.02971] that wormholes can arise from averages over states rather than theories. As an application, we calculate the size of the long-time correlation function $\langle A(t) A(0)\rangle$.

  4 citations