arXiv subjects

Fabian J. Pauw

Publications and source records attributed to Fabian J. Pauw.

4 recordsLinked to original sources

arXiv2026

Long-Range Order and Composite Boson Condensation in Lattice Quantum Hall States

Topological states of matter, such as quantum Hall states, are characterized by the absence of local order parameters. In the continuum, their topological order has been reinterpreted as the condensation of nonlocal composite bosons, but this condensation and the resulting long-range correlations have so far eluded direct confirmation beyond the simplest trial states. Here, we apply tensor-network methods to lattice Hamiltonians hosting quantum Hall states, revealing this exotic order directly in interacting ground states and demonstrating both the long-range correlations and the condensation of composite bosons. These correlations define a nonlocal order parameter that identifies phase transitions between trivial and topological phases, for both bosonic and fermionic models. The corresponding operators are accessible through site-resolved, local measurements on an extensive number of particles, making them directly probable in quantum simulators. Our work opens new avenues for microscopic studies of topological quantum matter beyond the reach of traditional solid-state approaches.

cond-mat.mes-hall↗

arXiv2026

Adaptive Pseudoboson Density-Matrix Renormalization Group for Dilute 2D Systems

Simulating strongly correlated systems in two dimensions is notoriously challenging due to rapid entanglement growth and frustration. Here, we introduce the adaptive projected-purified pseudoboson density-matrix renormalization group (A3P-DMRG) tailored to explore the ground states of dilute lattice models. The method compresses cluster Hilbert spaces by retaining only the most probable low-occupation Fock states, identified via probabilistic bounds and refined through a self-consistent mean-field basis optimization. We demonstrate that A3P-DMRG is advantageous in low-filling and weak-coupling regimes for large system sizes where conventional DMRG struggles. This establishes the method as a versatile tool for studying dilute quantum many-body systems relevant to ultra-cold atom quantum simulators, photonic lattices, Moiré materials and quantum chemistry.

cond-mat.str-el↗

arXiv2025

From hidden order to skyrmions: Quantum Hall states in an extended Hofstadter-Fermi-Hubbard model

The interplay between topology and strong interactions gives rise to a variety of exotic quantum phases, including fractional quantum Hall (FQH) states and their lattice analogs - fractional Chern insulators (FCIs). Such topologically ordered states host fractionalized excitations and, for spinful systems, are often accompanied by ferromagnetism and skyrmions. Here, we study a Hofstadter-Hubbard model of spinful fermions on a square lattice, extended by nearest-neighbor interactions. Using large-scale density matrix renormalization group (DMRG) simulations, we demonstrate the emergence of a spin-polarized $\frac{1}{3}$-Laughlin-like FCI phase, characterized by a quantized many-body Chern number, a finite charge gap, and hidden off-diagonal long-range order. We further investigate the quantum Hall ferromagnet at $ν=1$ and its skyrmionic excitations upon doping. In particular, we find that nearest-neighbor repulsion is sufficient to stabilize both particle- and hole-skyrmions in the ground state around $ν=1$, whereas we do not find such textures around $ν=\frac{1}{3}$. The diagnostic toolbox presented in this work, based on local densities, correlation functions, and spin-resolved observables, is directly applicable in quantum gas microscopy experiments. Our results open new pathways for experimental exploration of FCIs with spin textures in both ultracold atom and electronic systems.

cond-mat.quant-gas↗

arXiv2023

Detecting Hidden Order in Fractional Chern Insulators

Topological phase transitions go beyond Ginzburg and Landau's paradigm of spontaneous symmetry breaking and occur without an associated local order parameter. Instead, such transitions can be characterized by the emergence of non-local order parameters, which require measurements on extensively many particles simultaneously - an impossible venture in real materials. On the other hand, quantum simulators have demonstrated such measurements, making them prime candidates for an experimental confirmation of non-local topological order. Here, building upon the recent advances in preparing few-particle fractional Chern insulators using ultracold atoms and photons, we propose a realistic scheme for detecting the hidden off-diagonal long-range order (HODLRO) characterizing Laughlin states. Furthermore, we demonstrate the existence of this hidden order in fractional Chern insulators, specifically for the $ν=\frac{1}{2}$-Laughlin state in the isotropic Hofstadter-Bose-Hubbard model. This is achieved by large-scale numerical density matrix renormalization group (DMRG) simulations based on matrix product states, for which we formulate an efficient sampling procedure providing direct access to HODLRO in close analogy to the proposed experimental scheme. We confirm the characteristic power-law scaling of HODLRO, with an exponent $\frac{1}ν = 2$, and show that its detection requires only a few thousand snapshots. This makes our scheme realistically achievable with current technology and paves the way for further analysis of non-local topological orders, e.g. in topological states with non-Abelian anyonic excitations.

cond-mat.quant-gas↗