Competing topological orders in three dimensions: X-cube versus toric code - Mühlhauser, Matthias; Schmidt, Kai Phillip; Vidal, Julien; Walther, Matthias (SciPost Physics, 2022)
We study the competition between two different topological orders in three dimensions by considering the X-cube model and the three-dimensional toric code. The corresponding Hamiltonian can be decomposed into two commuting parts, one of which displays a self-dual spectrum. To determine the phase diagram, we compute the high-order series expansions of the ground-state energy in all limiting cases. Apart from the topological order related to the toric code and the fractonic order related to the X-cube model, we found two new phases which are adiabatically connected to classical limits with nontrivial sub-extensive degeneracies. All phase transitions are found to be first order.
CRIS-Team Scopus Importer:2022-03-25

Continuous similarity transformation for critical phenomena: Easy-axis antiferromagnetic XXZ model - Walther, Matthias; Hering, Dag-Bjoern; Uhrig, Goetz S.; Schmidt, Kai Phillip (Physical Review Research, 2023)
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 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.
CRIS-Team WoS Importer:2023-03-31

Extracting quantum-critical properties from directly evaluated enhanced perturbative continuous unitary transformations - Schamriß, Lukas; Walther, Matthias; Schmidt, Kai Phillip (SciPost Physics, 2024)
Directly evaluated enhanced perturbative continuous unitary transformations (deep-CUTs) are used to calculate non-perturbatively extrapolated numerical data for the ground-state energy and the energy gap. The data coincide with numerical evaluations of the truncated perturbative series and provide robust extrapolations beyond the perturbative regime. We develop a general scheme to extract quantum-critical properties from the deepCUT data based on critical scaling and a strict correspondence between the truncation used for deepCUT and the length scale of correlations at the critical point. We apply our approach to transverse-field Ising models (TFIMs) as paradigmatic systems for quantum phase transitions of various universality classes depending on the lattice geometry and the choice of antiferromagnetic or ferromagnetic coupling. In particular, we focus on the quantum phase diagram of the bilayer antiferromagnetic TFIM on the triangular lattice with an Ising-type interlayer coupling. Without a field, the model is known to host a classically disordered ground state, and in the limit of decoupled layers it exhibits the 3d-XY ’order by disorder’ transition of the corresponding single-layer model. Our starting point for the unknown parts of the phase diagram is a high-order perturbative calculation about the limit of isolated dimers where the model is in a gapped phase.
CRIS-Team Scopus Importer:2024-10-11

Quantitative description of long-range order in the spin- 12 XXZ antiferromagnet on the square lattice - Caci, Nils; Hering, Dag Björn; Walther, Matthias; Schmidt, Kai Phillip; Wessel, Stefan; Uhrig, Götz S. (Physical Review B, 2024)
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 quantum XXZ 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 semianalytic 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.
CRIS-Team Scopus Importer:2024-08-16

Quantum critical phase transition between two topologically ordered phases in the Ising tonic code bilayer - Wiedmann, Raymond; Lenke, Lea; Walther, Matthias; Mühlhauser, Matthias; Schmidt, Kai Phillip (Physical Review B, 2020)
We demonstrate that two toric code layers on the square lattice coupled by an Ising interaction display two distinct phases with intrinsic topological order. The second-order quantum phase transition between the weakly coupled Z(2) x Z(2) and the strongly coupled Z(2) topological order can be described by the condensation of bosonic quasiparticles from both sides and belongs to the three-dimensional Ising* universality class. This can be shown by an exact duality transformation to the transverse-field Ising model on the square lattice, which builds on the existence of an extensive number of local Z(2) conserved parities. These conserved quantities correspond to the product of two adjacent star operators on different layers. Notably, we show that the low-energy effective model derived about the limit of large Ising coupling is given by an effective single-layer toric code in terms of the conserved quantities of the Ising toric code bilayer. The two topological phases are further characterized by the topological entanglement entropy which serves as a nonlocal order parameter.
CRIS-Team WoS Importer:2021-01-08

Quantum melting of long-range ordered quantum antiferromagnets investigated by momentum-space continuous similarity transformations - Hering, Dag Björn; Walther, Matthias; Schmidt, Kai Phillip; Uhrig, Götz S. (Physical Review B, 2024)
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 J1-J2 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.
CRIS-Team Scopus Importer:2024-08-16

Quantum robustness of fracton phases - Mühlhauser, Matthias; Walther, Matthias; Reiss, D. A.; Schmidt, Kai Phillip (Physical Review B, 2020)
The quantum robustness of fracton phases is investigated by studying the influence of quantum fluctuations on the X-Cube model and Haah's code, which realize a type-I and type-II fracton phase, respectively. To this end, a finite uniform magnetic field is applied to induce quantum fluctuations in the fracton phase, resulting in zero-temperature phase transitions between fracton phases and polarized phases. Using high-order series expansions and a variational approach, all phase transitions are classified as strongly first order, which turns out to be a consequence of the (partial) immobility of fracton excitations. Indeed, single fractons as well as few-fracton composites can hardly lower their excitation energy by delocalization due to the intriguing properties of fracton phases, as demonstrated in this work explicitly in terms of fracton quasiparticles.
CRIS-Team WoS Importer:2020-03-06