arXiv subjects

Gunnar Möller

Publications and source records attributed to Gunnar Möller.

16 recordsLinked to original sources

arXiv2026

Dissociation of bulk and entanglement phase transitions in the Haldane phase

Quantum entanglement provides a sensitive probe of topological phases and strong correlations in quantum many-body systems. We revisit the momentum-resolved entanglement spectrum (ES) of the spin-$\frac12$ XXZ ladder in the Haldane phase, whose SU(2)-symmetric spectrum has for over fifteen years been interpreted as a single des Cloizeaux--Pearson mode. Using momentum-resolved entanglement spectroscopy based on exact diagonalization of ladders with up to 40 spins, we instead resolve two distinct modes crossing at $k=π/2$ and forming a sharp cusp rather than a single $\sin|k|$ branch, revising the SU(2)-symmetric ES. We then introduce explicit SU(2) symmetry breaking through an XXZ anisotropy. The ES undergoes a phase transition at the isotropic point, while the physical ladder remains in the Haldane phase until a distinct bulk transition at larger anisotropy, establishing a dissociation between bulk and entanglement phase transitions. Between the entanglement and bulk critical points, no gapless entanglement branch remains that can be interpreted as a Haldane-edge excitation, signalling breakdown of the Li--Haldane correspondence. In the easy-plane regime, the ES develops an Anderson tower of states, and the entanglement ground state exhibits long-ranged spin correlations on the finite chains studied, consistent with emergent U(1)-broken order and incompatible with conventional short-range one-dimensional Hamiltonians satisfying the assumptions underlying the Lieb--Schultz--Mattis and Mermin--Wagner--Hohenberg--Coleman theorems. Together, these results establish entanglement-only quantum criticality as a distinct manifestation of critical behaviour encoded in the entanglement description.

cond-mat.str-el↗

arXiv2026

Gauge-covariant projected entangled paired states for interacting systems in a magnetic field

The Hamiltonian for a system of itinerant particles on a two-dimensional lattice in a uniform magnetic field reduces the translational symmetry to a magnetic translation group, because of the need to choose a particular gauge for the vector potential. Nonetheless, in many situations all physical observables of the ground state remain entirely translation invariant. In this work, we introduce a projected entangled-pair state (PEPS) wavefunction with a pattern of virtual flux tensors, for which all physical expectation values are translation invariant by construction, possibly within an enlarged unit cell reflecting any symmetry breaking in the target state. Moreover, we show that the usual contraction and optimization methods for translation-invariant PEPS can be used, with the magnetic flux per plaquette only entering as a continuous parameter in the tensor network contractions. Therefore, our approach provides a method for simulating an interacting many-body system in a uniform magnetic field independently of the gauge choice for the vector potential and bypassing the need to consider extended magnetic unit cells.

quant-ph↗

arXiv2026

Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers

Dirac exceptional points (EPs) represent a novel class of non-Hermitian singularities that, unlike conventional EPs, reside entirely within the parity-time unbroken phase and exhibit linear energy dispersion. Here, we theoretically investigate the quantum geometry of Dirac EPs realized in nitrogen-vacancy centers in diamond, utilizing fidelity susceptibility as a probe. We demonstrate that despite the absence of a symmetry-breaking phase transition, the Dirac EP induces a pronounced geometric singularity, confirming the validity of the fidelity in characterizing non-Hermitian EPs. Specifically, the real part of the fidelity susceptibility diverges to negative infinity, which serves as a signature of non-Hermitian criticality. Crucially, however, we reveal that this divergence exhibits a distinct anisotropy, diverging along the non-reciprocal coupling direction while remaining finite along the detuning axis. Furthermore, we establish that this anisotropy, characterized by at least one exact dark direction coexisting with divergent directions, is a generic consequence of the Dirac EP structure whenever the parameter derivatives collectively span the off-diagonal operator space at the Dirac EP. This behavior stands in stark contrast to the omnidirectional divergence observed in conventional EPs. Our findings provide a comprehensive picture of the fidelity probe near the Dirac EP, highlighting the critical role of parameter directionality in exploiting Dirac EPs for quantum control and sensing applications.

quant-ph↗

arXiv2025

Fitness landscape for quantum state tomography from neutron scattering

Recently, a direct connection between static structure factors and quantum ground states for two-spin interaction Hamiltonians was proven. This suggests the possibility of quantum state tomography from neutron scattering. Here, we investigate the associated fitness landscape numerically. We find a linear relationship between the mean square distances of the structure factors and the associated state overlaps, implying a well-behaved fitness landscape. Furthermore, we find evidence suggesting that the approach can be generalized to thermal equilibrium states. We also extend the arguments to the cases of applied magnetic fields and finite clusters.

cond-mat.str-el↗

arXiv2024

Tensor Network Python (TeNPy) version 1

TeNPy (short for 'Tensor Network Python') is a python library for the simulation of strongly correlated quantum systems with tensor networks. The philosophy of this library is to achieve a balance of readability and usability for new-comers, while at the same time providing powerful algorithms for experts. The focus is on MPS algorithms for 1D and 2D lattices, such as DMRG ground state search, as well as dynamics using TEBD, TDVP, or MPO evolution. This article is a companion to the recent version 1.0 release of TeNPy and gives a brief overview of the package.

cond-mat.str-el↗

arXiv2023

Energy minimization of paired composite fermion wave functions in the spherical geometry

We perform the energy minimization of the paired composite fermion (CF) wave functions, proposed by Möller and Simon (MS) [PRB 77, 075319 (2008)] and extended by Yutushui and Mross (YM) [PRB 102, 195153 (2020)], where the energy is minimized by varying the CF pairing function, in the case of an approximate model of the Coulomb interaction in the second Landau level for pairing channels $\ell = -1, 3, 1$ which are expected to be in the Pfaffian, anti-Pfaffian and particle-hole symmetric (PH) Pfaffian phases respectively. It is found that the energy of the $\ell = -1$ MS wave function can be reduced substantially below that of the Moore-Read wave function at small system sizes, however, in the $\ell = 3$ case the energy cannot be reduced much below that of the YM trial wavefunction. Nonetheless, both our optimized and unoptimized wavefunctions with $\ell=-1,3$ extrapolate to roughly the same energy per particle in the thermodynamic limit. For the $\ell = 1$ case, the optimization makes no qualitative difference and these PH-Pfaffian wave functions are still energetically unfavourable. The effective CF pairing is analyzed in the resulting wave functions, where the effective pairing for the $\ell = -1, 3$ channels is found to be well approximated by a weak-pairing BCS ansatz and the $\ell = 1$ wave functions show no sign of emergent CF pairing.

cond-mat.str-el↗

arXiv2023

Self-similarity of spectral response functions for fractional quantum Hall states

Spectral response functions are central quantities in the analysis of quantum many-body states, since they describe the response of many-body systems to external perturbations and hence directly correspond to observables in experiments. In this paper, we evaluate a momentum-averaged dynamical density structure factor for the fermionic $ν=1/3$ fractional quantum Hall state on a torus, using the continued fraction method to compute the dynamical correlation function. We establish the scaling behavior of the screened Coulomb structure factor with respect to interaction range, and expose an inherent self-similarity of structure factors in the frequency domain. These results highlight the statistical properties of spectral response functions for fractional quantum Hall states and show how they can be efficiently approximated in numerical models.

cond-mat.str-el↗

arXiv2022

Interaction-driven plateau transition between integer and fractional Chern Insulators

We present numerical evidence of an interaction-driven quantum Hall plateau transition between a $|C|>1$ Chern Insulator (CI) and a $ν= 1/3$ Laughlin state in the Harper-Hofstadter model. We study the model at flux densities $p/q$, where the lowest Landau level (LLL) manifold comprises $p$ magnetic sub-bands. For weak interactions, the model realises integer CIs corresponding to filled sub-bands, while strongly interacting candidate states include fractional quantum Hall (FQH) states at LLL filling fractions $ν=r/t$. These phases may compete at the same particle density when $p=t$. As a concrete example, we numerically explore the physics at flux density $n_ϕ = 3/11$, where we show evidence that a direct transition occurs between a CI and a $ν= 1/3$ Laughlin state, which we characterise in terms of its critical, topological and entanglement properties. We also show that strong interactions generically stabilise a $ν= 1/3$ Laughlin state even when the LLL is split into multiple bands, and introduce a powerful methodology to extract its topological entanglement entropy by exploiting the scaling of magnetic length with $n_ϕ$.

cond-mat.str-el↗

arXiv2021

Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model

The Hofstadter model is a popular choice for theorists investigating the fractional quantum Hall effect on lattices, due to its simplicity, infinite selection of topological flat bands, and increasing applicability to real materials. In particular, fractional Chern insulators in bands with Chern number $|C|>1$ can demonstrate richer physical properties than continuum Landau level states and have recently been detected in experiments. Motivated by this, we examine the stability of fractional Chern insulators with higher Chern number in the Hofstadter model, using large-scale infinite density matrix renormalization group simulations on a thin cylinder. We confirm the existence of fractional states in bands with Chern numbers $C=1,2,3,4,5$ at the filling fractions predicted by the generalized Jain series [Phys. Rev. Lett. 115, 126401 (2015)]. Moreover, we discuss their metal-to-insulator phase transitions, as well as the subtleties in distinguishing between physical and numerical stability. Finally, we comment on the relative suitability of fractional Chern insulators in higher Chern number bands for proposed modern applications.

cond-mat.str-el↗

arXiv2018

Synthetic Gauge Fields for Lattices with Multi-Orbital Unit Cells: Routes towards a $π$-flux Dice Lattice with Flat Bands

We propose a general strategy for generating synthetic magnetic fields in complex lattices with non-trivial connectivity based on light-matter coupling in cold atomic gases. Our approach starts from an underlying optical flux lattice in which flux arises by coupling several internal states. Starting from a high symmetry optical flux lattice, we superpose a scalar potential with a super- or sublattice period in order to eliminate links between the original lattice sites. As an alternative to changing connectivity, the approach can also be used to create or remove lattice sites from the underlying parent lattice. To demonstrate our concept, we consider the dice lattice geometry as an explicit example, and construct a dice lattice with a flux density of half a flux quantum per plaquette, providing a pathway to flat bands with a large band gap. While the intuition for our proposal stems from analysis of deep optical lattices, we demonstrate that the approach is robust even for shallow optical flux lattices far from the tight-binding limit. We also provide an alternative experimental proposal to realize a synthetic gauge field in a fully frustrated dice lattice based on laser-induced hoppings along individual bonds of the lattice, again involving a superlattice potential. In this approach, atoms with a long-lived excited state are trapped using an 'anti-magic' wavelength of light, allowing the desired complex hopping elements to be induced in a specific laser coupling scheme for the dice lattice geometry. We conclude by comparing the complexity of these alternative approaches, and advocate that complex optical flux lattices provide the more elegant and easily generalisable strategy.

cond-mat.quant-gas↗

arXiv2018

Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$

We study the stability of composite fermion fractional quantum Hall states in Harper-Hofstadter bands with Chern number $|C|>1$. We analyze the states of the composite fermion series for bosons with contact interactions and (spinless) fermions with nearest-neighbor interactions. We examine the scaling of the many-body gap as the bands are tuned to the effective continuum limit $n_ϕ\to 1/|C|$. Near these points, the Hofstadter model realises large magnetic unit cells that yield bands with perfectly flat dispersion and Berry curvature. We exploit the known scaling of energies in the effective continuum limit in order to maintain a fixed square aspect ratio in finite-size calculations. Based on exact diagonalization calculations of the band-projected Hamiltonian, we show that almost all finite-size spectra yield the ground-state degeneracy predicted by composite fermion theory. We confirm that states at low ranks in the composite fermion hierarchy are the most robust and yield a clear gap in the thermodynamic limit. For bosons in $|C|=2$ and $|C|=3$ bands, our data for the composite fermion states are compatible with a finite gap in the thermodynamic limit. We also report new evidence for gapped incompressible states of fermions in $|C|>1$ bands, which have large entanglement gaps. For cases with a clear spectral gap, we confirm that the thermodynamic limit commutes with the effective continuum limit. We analyze the nature of the correlation functions for the Abelian composite fermion states and find that they feature $|C|^2$ smooth sheets. We examine two cases associated with a bosonic integer quantum Hall effect (BIQHE): For $ν=2$ in $|C|=1$ bands, we find a strong competing state with a higher ground-state degeneracy, so no clear BIQHE is found in the band-projected Hofstadter model; for $ν=1$ in $|C|=2$ bands, we present additional data confirming the existence of a BIQHE state.

cond-mat.str-el↗

arXiv2017

Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States

We investigate extrinsic wormholelike twist defects that effectively increase the genus of space in lattice versions of multicomponent fractional quantum Hall systems. Although the original band structure is distorted by these defects, leading to localized midgap states, we find that a new lowest flat band representing a higher genus system can be engineered by tuning local single-particle potentials. Remarkably, once local many-body interactions in this new band are switched on, we identify various Abelian and non-Abelian fractional quantum Hall states, whose ground-state degeneracy increases with the number of defects, i.e, with the genus of space. This sensitivity of topological degeneracy to defects provides a "proof of concept" demonstration that genons, predicted by topological field theory as exotic non-Abelian defects tied to a varying topology of space, do exist in realistic microscopic models. Specifically, our results indicate that genons could be created in the laboratory by combining the physics of artificial gauge fields in cold atom systems with already existing holographic beam shaping methods for creating twist defects.

cond-mat.str-el↗

arXiv2016

Magnetic diffuse scattering in artificial kagome spin ice

The study of magnetic correlations in dipolar-coupled nanomagnet systems with synchrotron x-ray scattering provides a means to uncover emergent phenomena and exotic phases, in particular in systems with thermally active magnetic moments. From the diffuse signal of soft x-ray resonant magnetic scattering, we have measured magnetic correlations in a highly dynamic artificial kagome spin ice with sub-70-nm Permalloy nanomagnets. On comparing experimental scattering patterns with Monte Carlo simulations based on a needle-dipole model, we conclude that kagome ice I phase correlations exist in our experimental system even in the presence of moment fluctuations, which is analogous to bulk spin ice and spin liquid behavior. In addition, we describe the emergence of quasi-pinch-points in the magnetic diffuse scattering in the kagome ice I phase. These quasi-pinch-points bear similarities to the fully developed pinch points with singularities of a magnetic Coulomb phase, and continually evolve into the latter on lowering the temperature. The possibility to measure magnetic diffuse scattering with soft x rays opens the way to study magnetic correlations in a variety of nanomagnetic systems.

cond-mat.mes-hall↗

arXiv2015

Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number

The Harper-Hofstadter model provides a fractal spectrum containing topological bands of any integer Chern number, $C$. We study the many-body physics that is realized by interacting particles occupying Harper-Hofstadter bands with $|C|>1$. We formulate the predictions of Chern-Simons or composite fermion theory in terms of the filling factor, $ν$, defined as the ratio of particle density to the number of single-particle states per unit area. We show that this theory predicts a series of fractional quantum Hall states with filling factors $ν= r/(r|C| +1)$ for bosons, or $ν= r/(2r|C| +1)$ for fermions. This series includes a bosonic integer quantum Hall state (bIQHE) in $|C|=2$ bands. We construct specific cases where a single band of the Harper-Hofstadter model is occupied. For these cases, we provide numerical evidence that several states in this series are realized as incompressible quantum liquids for bosons with contact interactions.

cond-mat.str-el↗

arXiv2014

Josephson Coupled Moore-Read States

We study a quantum Hall bilayer system of bosons at total filling factor $ν= 1$, and study the phase that results from short ranged pair-tunneling combined with short ranged interlayer interactions. We introduce two exactly solvable model Hamiltonians which both yield the coupled Moore-Read state [Phys.~Rev.~Lett.~{\bf 108}, 256809 (2012)] as a ground state, when projected onto fixed particle numbers in each layer. One of these Hamiltonians describes a gapped topological phase while the other is gapless. However, on introduction of a pair tunneling term, the second system becomes gapped and develops the same topological order as the gapped Hamiltonian. Supported by the exact solution of the full zero-energy quasihole spectrum and a conformal field theory approach, we develop an intuitive picture of this system as two coupled composite fermion superconductors. In this language, pair tunneling provides a Josephson coupling of the superconducting phases of the two layers, and gaps out the Goldstone mode associated with particle transport between the layers. In particular, this implies that quasiparticles are confined between the layers. In the bulk, the resulting phase has the topological order of the Halperin 220 phase with $U(1)_2\times U(1)_2$ topological order, but it is realized in the symmetric/antisymmetric-basis of the layer index. Consequently, the edge spectrum at a fixed particle number reveals an unexpected $U(1)_4 \times U(1)$ structure.

cond-mat.mes-hall↗

arXiv2014

Majorana modes and $p$-wave superfluids for fermionic atoms in optical lattices

We present a simple approach to create a strong $p$-wave interaction for fermions in an optical lattice. The crucial step is that the combination of a lattice setup with different orbital states and $s$-wave interactions can give rise to a strong induced $p$-wave pairing. We identify different topological phases and demonstrate that the setup offers a natural way to explore the transition from Kitaev's Majorana wires to two-dimensional $p$-wave superfluids. We demonstrate how this design can induce Majorana modes at edge dislocations in the optical lattice, and we provide an experimentally feasible protocol for the observation of the non-Abelian statistics.

cond-mat.quant-gas↗