Absence of fractal quantum criticality in the quantum Newman-Moore model - Wiedmann, Raymond; Lenke, Lea; Mühlhauser, Matthias; Schmidt, Kai Phillip (Physical Review Research, 2024)
The quantum phase transition between the low-field fracton phase with type-II fracton excitations and the high-field polarized phase is investigated in the two-dimensional self-dual quantum Newman-Moore model. We apply perturbative and numerical linked-cluster expansions to calculate the ground-state energy per site in the thermodynamic limit, revealing a level crossing at the self-dual point. In addition, high-order series expansions of the relevant low-energy gaps are determined using perturbative continuous unitary transformations indicating no gap closing. Our results therefore predict a first-order phase transition between the low-field fracton and the high-field polarized phase at the self-dual point.<br

High-order series expansion of non-Hermitian quantum spin models - Lenke, Lea; Mühlhauser, Matthias; Schmidt, Kai Phillip (Physical Review B, 2021)
We investigate the low-energy physics of non-Hermitian quantum spin models with PT symmetry. To this end, we consider the one-dimensional Ising chain and the two-dimensional toric code in a non-Hermitian staggered field. For both systems, dual descriptions in terms of non-Hermitian staggered Ising interactions in a conventional transverse field exist. We perform high-order series expansions about the high- and low-field limit for both systems to determine the ground-state energy per site and the one-particle gap. The one-dimensional non-Hermitian Ising chain is known to be exactly solvable. Its ground-state phase diagram consists of second-order quantum phase transitions, which can be characterized by logarithmic singularities of the second derivative of the ground-state energy and, in the symmetry-broken phase, the gap closing of the low-field gap. In contrast, the gap closing from the high-field phase is not accessible perturbatively due to the complex energy and the occurrence of exceptional lines in the high-field gap expression. For the two-dimensional toric code in a non-Hermitian staggered field, we study the quantum robustness of the topologically ordered phase by the gap closing of the low-field gap. We find that the well-known second-order quantum phase transition of the toric code in a uniform field extends into a large portion of the non-Hermitian parameter space. However, the series expansions become unreliable for a dominant anti-Hermitian field. Interestingly, the analysis of the high-field gap reveals the potential presence of an intermediate region.
CRIS-Team Scopus Importer:2021-12-17

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 phase transitions in the K-layer Ising toric code - Schamriss, Lukas; Lenke, Lea; Mühlhauser, Matthias; Schmidt, Kai Phillip (Physical Review B, 2022)
We investigate the quantum phase diagram of the K-layer Ising toric code corresponding to K layers of twodimensional toric codes coupled by Ising interactions. While for small Ising interactions the system displays 1K2 topological order originating from the toric codes in each layer, the system shows 12 topological order in the high-Ising limit. The latter is demonstrated for general K by deriving an effective low-energy model in Kth-order degenerate perturbation theory, which is given as an effective anisotropic single-layer toric code in terms of collective pseudospins 1/2 referring to the two ground states of isolated Ising chain segments. For the specific cases K = 3 and K = 4 we apply high-order series expansions to determine the gap series in the low- and high-Ising limit. Extrapolation of the elementary energy gaps gives convincing evidence that the ground-state phase diagram consists of a single quantum critical point and our findings suggest a quantum phase transition in the 3D Ising* universality class for both K separating both types of topological order, which is consistent with former findings for the bilayer Ising toric code.
CRIS-Team WoS Importer:2022-07-01

Series expansions in closed and open quantum many-body systems with multiple quasiparticle types - Lenke, Lea; Schellenberger, Andreas; Schmidt, Kai Phillip (Physical Review A, 2023)
The established approach of perturbative continuous unitary transformations (pCUTs) constructs effective quantum many-body Hamiltonians as perturbative series that conserve the number of one quasiparticle type. We extend the pCUT method to similarity transformations - dubbed pcst++ - allowing for multiple quasiparticle types with complex-valued energies. This enlarges the field of application to closed and open quantum many-body systems with unperturbed operators corresponding to arbitrary superimposed ladder spectra. To this end, a generalized counting operator is combined with the quasiparticle generator for open quantum systems recently introduced by Schmiedinghoff and Uhrig [G. Schmiedinghoff and G. S. Uhrig, SciPost Phys. 13, 122 (2022)2542-465310.21468/SciPostPhys.13.6.122]. The pcst++ then yields model-independent block-diagonal effective Hamiltonians and Lindbladians, allowing a linked-cluster expansion in the thermodynamic limit similar to the conventional pCUT method. We illustrate the application of the pcst++ method by discussing representative closed, open, and non-Hermitian quantum systems.
CRIS-Team Scopus Importer:2023-08-18