arXiv subjects

Kai P. Schmidt

Publications and source records attributed to Kai P. Schmidt.

At least 19 recordsLinked to original sources

arXiv2026

Unconventional entanglement scaling and quantum criticality in the long-range spin-one Heisenberg chain with single-ion anisotropy

Long-range interactions can fundamentally reshape the low-energy properties of low-dimensional quantum matter, altering both continuous symmetry breaking and topological phenomena. However, their impact on the quantum criticality separating these regimes remains poorly understood. We determine the ground-state phase diagram and critical properties of the spin-one Heisenberg chain with single-ion anisotropy and staggered antiferromagnetic power-law interactions, using matrix-product state (MPS) calculations complemented by high-order series expansions (pCUT+MC). Such long-range, non-frustrated interactions circumvent the Hohenberg-Mermin-Wagner theorem, thereby stabilizing continuous symmetry breaking (CSB) phases in direct competition with the Haldane phase. We map out the resulting phase diagram and analyze the entanglement entropy scaling behavior in the U(1) and SU(2) CSB phases, finding logarithmic corrections beyond the short-range, universal contributions expected from linearly dispersed Goldstone modes. We further characterize all critical boundaries through finite-size scaling of either the entanglement entropy or the staggered magnetization. In particular, the large-D-to-U(1)-CSB transition exhibits unconventional, continuously varying critical exponents as a function of the long-range decay exponent with a strong dependence on the imposed boundary conditions leading to distinct finite-size scalings for sufficiently long-range potentials. Remarkably, the Haldane-to-U(1)-CSB transition likewise displays unconventional quantum criticality with distinct continuously varying critical exponents. Our work positions this model as a target for near-term atomic platforms with tunable long-range couplings and exhibiting natural single-ion anisotropy, offering a minimal playground for exploring the interplay between long-range interactions, continuous symmetry breaking, and topology.

cond-mat.str-el↗

arXiv2026

To infinity and back -- $1/N$ graph expansions of light-matter systems

We present a method for performing a full graph expansion for light-matter systems, utilizing the linked-cluster theorem. This method enables us to explore $1/N$ corrections to the thermodynamic limit $N\to \infty$ in the number of particles, giving us access to the mesoscopic regime. While this regime is yet largely unexplored due to the challenges of studying it with established approaches, it incorporates intriguing features, such as entanglement between light and matter that vanishes in the thermodynamic limit. As a representative application, we calculate physical quantities of the low-energy regime for the paradigmatic Dicke-Ising chain in the paramagnetic normal phase by accompanying the graph expansion with both exact diagonalization (NLCE) and perturbation theory (pcst++), benchmarking our approach against other techniques. We investigate the ground-state energy density and photon density, showing a smooth transition from the microscopic to the macroscopic regime up to the thermodynamic limit. Around the quantum critical point, we extract the $1/N$ corrections to the ground-state energy density to obtain the critical point and critical exponent using extrapolation techniques.

cond-mat.str-el↗

arXiv2025

Quantum effects in the magnon spectrum of 2D altermagnets via continuous similarity transformations

We investigate quantum effects on magnon excitations in a minimal spin-1/2 Heisenberg model for 2D altermagnets on the square lattice. A continuous similarity transformation is applied in momentum space to derive an effective Hamiltonian that conserves the number of magnon excitations. This allows us to quantitatively calculate the one-magnon dispersion, the effects of magnon-magnon interactions, and the dynamic structure factor in a certain range of parameters. In particular, we focus on the altermagnetic spin splitting of the magnon bands and the size of the roton minimum. We further map out divergencies of the continuous similarity transformation for different types of generators, which signal either the breakdown of the Néel-ordered phase or the presence of significant magnon decay.

cond-mat.str-el↗

arXiv2024

Quantum melting of long-range ordered quantum antiferromagnets investigated by momentum-space continuous similarity transformations

We apply continuous similarity transformations (CSTs) to study the zero-temperature breakdown of long-range ordered quantum antiferromagnets. The CST flow equations are truncated in momentum space by the scaling dimension so that all operators with scaling dimension up to two are taken into account. We determine the quantum phase transition out of the Néel-ordered phase in the unfrustrated square lattice Heisenberg bilayer as well as the quantum melting of the Néel-ordered and columnar phase in the highly frustrated $J_1$-$J_2$ model on the square lattice. In all cases the CST is set up to isolate the ground state so that the stability of the flow equations, the ground-state energy, and the sublattice magnetization are used to explore the long-range ordered phases. We extract quantum-critical points which agree well with values in the literature. Further, we estimate the associated critical exponents $α$ and $β$ which turns out to be a challenging task for the CST approach.

cond-mat.str-el↗

arXiv2024

Quantitative description of long-range order in the anisotropic spin-1/2 Heisenberg antiferromagnet on the square lattice

The quantitative description of long-range order remains a challenge in quantum many-body physics. We provide zero-temperature results from two complementary methods for the ground-state energy per site, the sublattice magnetization, the spin gap, and the transverse spin correlation length for the spin-1/2 anisotropic quantum Heisenberg antiferromagnet on the square lattice. On the one hand, we use exact, large-scale quantum Monte Carlo (QMC) simulations. On the other hand, we use the semi-analytic approach based on continuous similarity transformations in terms of elementary magnon excitations. Our findings confirm the applicability and quantitative validity of both approaches along the full parameter axis from the Ising point to the symmetry-restoring phase transition at the Heisenberg point and further provide quantitative reference results in the thermodynamic limit. In addition, we analytically derive the relation between the dispersion and the correlation length at zero temperature in arbitrary dimension, and discuss improved second-moment QMC estimators.

cond-mat.str-el↗

arXiv2023

Metasurface-based hybrid optical cavities for chiral sensing

Quantum metasurfaces, i.e., two-dimensional subwavelength arrays of quantum emitters, can be employed as mirrors towards the design of hybrid cavities, where the optical response is given by the interplay of a cavity-confined field and the surface modes supported by the arrays. We show that, under external magnetic field control, stacked layers of quantum metasurfaces can serve as helicity-preserving cavities. These structures exhibit ultranarrow resonances and can enhance the intensity of the incoming field by orders of magnitude, while simultaneously preserving the handedness of the field circulating inside the resonator, as opposed to conventional cavities. The rapid phase shift in the cavity transmission around the resonance can be exploited for the sensitive detection of chiral scatterers passing through the cavity. We discuss possible applications of these resonators as sensors for the discrimination of chiral molecules.

quant-ph↗

arXiv2022

Continuous similarity transformation for critical phenomena: easy-axis antiferromagnetic XXZ model

We apply continuous similarity transformations (CSTs) to the easy-axis antiferromagnetic XXZ-model on the square lattice. The CST flow equations are truncated in momentum space by the scaling dimension $d$ so that all contributions with $d\le 2$ are taken into account. The resulting quartic magnon-conserving effective Hamiltonian is analyzed in the zero-, one-, and two-magnon sector. In this way, a quantitative description of the ground-state energy, the one-magnon dispersion and its gap as well as of two-magnon bound states is gained for anisotropies ranging from the gapped Ising model to the gapless Heisenberg model. We discuss the critical properties of the gap closing as well as the evolution of the one-magnon roton mininum. The excitation energies of two-magnon bound states are calculated and their decay into the two-magnon continuum is determined via the inverse participation ratio.

cond-mat.str-el↗

arXiv2022

Linear optical elements based on cooperative subwavelength emitter arrays

We describe applications of two-dimensional subwavelength quantum emitter arrays as efficient optical elements in the linear regime. For normally incident light, the cooperative optical response, stemming from emitter-emitter dipole exchanges, allows the control of the array's transmission, its resonance frequency, and bandwidth. Operations on fully polarized incident light, such as generic linear and circular polarizers as well as phase retarders can be engineered and described in terms of Jones matrices. Our analytical approach and accompanying numerical simulations identify optimal regimes for such operations and reveal the importance of adjusting the array geometry and of the careful tuning of the external magnetic fields amplitude and direction.

quant-ph↗

arXiv2022

Evidence for pressure induced unconventional quantum criticality in the coupled spin ladder antiferromagnet C$_9$H$_{18}$N$_2$CuBr$_4$

Quantum phase transitions in quantum matter occur at zero temperature between distinct ground states by tuning a nonthermal control parameter. Often, they can be accurately described within the Landau theory of phase transitions, similarly to conventional thermal phase transitions. However, this picture can break down under certain circumstances. Here, we present a comprehensive study of the effect of hydrostatic pressure on the magnetic structure and spin dynamics of the spin-1/2 ladder compound C$_9$H$_{18}$N$_2$CuBr$_4$. Single-crystal heat capacity and neutron diffraction measurements reveal that the N$\rm \acute{e}$el-ordered phase breaks down beyond a critical pressure of $P_{\rm c}$$\sim$1.0 GPa through a continuous quantum phase transition. Estimates of the critical exponents suggest that this transition may fall outside the traditional Landau paradigm. The inelastic neutron scattering spectra at 1.3 GPa are characterized by two well-separated gapped modes, including one continuum-like and another resolution-limited excitation in distinct scattering channels, which further indicates an exotic quantum-disordered phase above $P_{\rm c}$.

cond-mat.str-el↗

arXiv2018

The Higgs Mode of Planar Coupled Spin-Ladders and its Observation in C$_9$H$_{18}$N$_2$CuBr$_4$

Polarized inelastic neutron scattering experiments recently identified the amplitude (Higgs) mode in C$_9$H$_{18}$N$_2$CuBr$_4$, a two-dimensional near-quantum-critical spin-1/2 two-leg ladder compound, which exhibits a weak easy-axis exchange anisotropy. Here, we theoretically examine the dynamic spin structure factor of such planar coupled spin-ladder systems using large-scale quantum Monte Carlo simulations. This allows us to provide a quantitative account of the experimental neutron scattering data within a consistent quantum spin model. Moreover, we trance the details of the continuous evolution of the amplitude mode from a two-particle bound state of coupled ladders in the classical Ising limit all the way to the quantum spin-1/2 Heisenberg limit with fully restored SU(2) symmetry, where it gets overdamped by the two-magnon continuum in neutron scattering.

cond-mat.str-el↗

arXiv2018

Bilayer Kitaev models: Phase diagrams and novel phases

Kitaev's honeycomb-lattice spin-$1/2$ model has become a paradigmatic example for $\mathbb{Z}_2$ quantum spin liquids, both gapped and gapless. Here we study the fate of these spin-liquid phases in differently stacked bilayer versions of the Kitaev model. Increasing the ratio between the inter-layer Heisenberg coupling $J_\perp$ and the intra-layer Kitaev couplings $K^{x,y,z}$ destroys the topological spin liquid in favor of a paramagnetic dimer phase. We study phase diagrams as a function of $J_\perp/K$ and Kitaev coupling anisotropies using Majorana-fermion mean-field theory, and we employ different expansion techniques in the limits of small and large $J_\perp/K$. For strongly anisotropic Kitaev couplings, we derive effective models for the different layer stackings which we use to discuss the quantum phase transition out of the Kitaev phase. We find that the phase diagrams depend sensitively on the nature of the stacking and anisotropy strength. While in some stackings and at strong anisotropies we find a single transition between the Kitaev and dimer phases, other stackings are more involved: Most importantly, we prove the existence of two novel macro-spin phases which can be understood in terms of Ising chains which can be either coupled ferromagnetically or remain degenerate, thus realizing a classical spin liquid. In addition, our results suggest the existence of a flux phase with spontaneous inter-layer coherence.

cond-mat.str-el↗

arXiv2017

Direct observation of the Higgs amplitude mode in a two-dimensional quantum antiferromagnet near the quantum critical point

Spontaneous symmetry-breaking quantum phase transitions play an essential role in condensed matter physics. The collective excitations in the broken-symmetry phase near the quantum critical point can be characterized by fluctuations of phase and amplitude of the order parameter. The phase oscillations correspond to the massless Nambu$-$Goldstone modes whereas the massive amplitude mode, analogous to the Higgs boson in particle physics, is prone to decay into a pair of low-energy Nambu$-$Goldstone modes in low dimensions. Especially, observation of a Higgs amplitude mode in two dimensions is an outstanding experimental challenge. Here, using the inelastic neutron scattering and applying the bond-operator theory, we directly and unambiguously identify the Higgs amplitude mode in a two-dimensional S=1/2 quantum antiferromagnet C$_9$H$_{18}$N$_2$CuBr$_4$ near a quantum critical point in two dimensions. Owing to an anisotropic energy gap, it kinematically prevents such decay and the Higgs amplitude mode acquires an infinite lifetime.

cond-mat.str-el↗

arXiv2016

Emergence of a 2d macro-spin liquid in a highly frustrated 3d quantum magnet

The classical Ising model on the frustrated 3d swedenborgite lattice has disordered spin liquid ground states for all ratios of inter- and intra-planar couplings. Quantum fluctuations due to a transverse field give rise to several exotic quantum phenomena. In the limit of weakly coupled Kagomé layers we find a 3d version of disorder by disorder. For large out-of-plane couplings 1d macro-spins are formed which realize a disordered macro-spin liquid on an emerging triangular lattice. Signatures of this dimensional reduction are also found in critical exponents of the quantum phase transition out of the fully polarized phase into the macro-spin liquid displaying quantum criticality typical for 2d quantum systems.

cond-mat.str-el↗

arXiv2015

Non-linear bond-operator theory and 1/d expansion for coupled-dimer magnets I: Paramagnetic phase

For coupled-dimer Heisenberg magnets, a paradigm of magnetic quantum phase transitions, we develop a systematic expansion in 1/d, the inverse number of space dimensions. The expansion employs a formulation of the bond-operator technique and is based on the observation that a suitably chosen product-state wavefunction yields exact zero-temperature expectation values of local observables in the d->infty limit, with corrections vanishing as 1/d. We demonstrate the approach for a model of dimers on a hypercubic lattice, which generalizes the square-lattice bilayer Heisenberg model to arbitrary d. In this paper, we use the 1/d expansion to calculate static and dynamic observables at zero temperature in the paramagnetic singlet phase, up to the quantum phase transition, and compare the results with numerical data available for d=2. Contact is also made with previously proposed refinements of bond-operator theory as well as with a perturbative expansion in the inter-dimer coupling. In a companion paper, the present 1/d expansion will be extended to the ordered phase, where it is shown to consistently describe the entire phase diagram including the quantum critical point.

cond-mat.str-el↗

arXiv2014

Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice in a magnetic field

Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice with Heisenberg intra-dimer and Ising inter-dimer couplings are found by two independent rigorous procedures. The first method uses a unitary transformation to establish a mapping correspondence with an effective classical spin model, while the second method relies on the derivation of an effective hard-core boson model by continuous unitary transformations. Both methods lead to equivalent effective Hamiltonians providing a convincing proof that the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice exhibits a zero-temperature magnetization curve with just two intermediate plateaus at one-third and one-half of the saturation magnetization, which correspond to stripe and checkerboard orderings of singlets and polarized triplets, respectively. The nature of the remarkable stripe order relevant to the one-third plateau is thoroughly investigated with the help of the corresponding exact eigenvector. The rigorous results for the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice are compared with the analogous results for the purely classical Ising and fully quantum Heisenberg models. Finally, we discuss to what extent the critical fields of SrCu2(BO3)2 and (CuCl)Ca2Nb3O10 can be described within the suggested Ising-Heisenberg model.

cond-mat.stat-mech↗

arXiv2011

Unconventional magnetization plateaus in a Shastry-Sutherland spin tube

Using density matrix renormalization group (DMRG) and perturbative continuous unitary transformations (PCUTs), we study the magnetization process in a magnetic field for all coupling strengths of a quasi-1D version of the 2D Shastry-Sutherland lattice, a frustrated spin tube made of two orthogonal dimer chains. At small inter-dimer coupling, plateaus in the magnetization appear at 1/6, 1/4, 1/3, 3/8, and 1/2. As in 2D, they correspond to a Wigner crystal of triplons. However, close to the boundary of the product singlet phase, plateaus of a new type appear at 1/5 and 3/4. They are stabilized by the localization of {\it bound states} of triplons. Their magnetization profile differs significantly from that of single triplon plateaus and leads to specific NMR signatures. We address the possibility to stabilize such plateaus in further geometries by analyzing small finite clusters using exact diagonalizations and the PCUTs.

cond-mat.other↗

arXiv2008

Solids and supersolids of three-body interacting polar molecules in an optical lattice

We study the physics of cold polar molecules loaded into an optical lattice in the regime of strong three-body interactions, as put forward recently by Büchler [Nature Phys. 3, 726 (2007)]. To this end quantum Monte Carlo simulations, exact diagonalization and a semiclassical approach are used to explore hardcore bosons on the two-dimensional square lattice which interact solely by long ranged three-body terms. The resulting phase diagram shows a sequence of solid and supersolid phases. Our findings are directly relevant for future experimental implementations and open a new route towards the discovery of a lattice supersolid phase in experiment.

cond-mat.str-el↗

arXiv2008

Supersolid phase induced by correlated hopping in spin-1/2 frustrated quantum magnets

We show that correlated hopping of triplets, which is often the dominant source of kinetic energy in dimer-based frustrated quantum magnets, produces a remarkably strong tendency to form supersolid phases in a magnetic field. These phases are characterized by simultaneous modulation and ordering of the longitudinal and transverse magnetization respectively. Using Quantum Monte Carlo and a semiclassical approach for an effective hard-core boson model with nearest-neighbor repulsion on a square lattice, we prove in particular that a supersolid phase can exist even if the repulsion is not strong enough to stabilize an insulating phase at half-filling. Experimental implications for frustrated quantum antiferromagnets in a magnetic field at zero and finite temperature are discussed.

cond-mat.str-el↗