Related papers: Two-Dimensional Density-Matrix Topological Fermion…
Two indicators of finite-temperature topological properties based on the Uhlmann connection, one generalizing the Wilson loop to the Uhlmann-Wilson loop and the other generalizing the Berry phase to the Uhlmann phase, are constructed…
The topological classification of fermion systems in mixed states is a long standing quest. For Gaussian states, reminiscent of non-interacting unitary fermions, some progress has been made. While the topological quantization of certain…
We define and compute many-body topological invariants of interacting fermionic symmetry-protected topological phases, protected by an orientation-reversing symmetry, such as time-reversal or reflection symmetry. The topological invariants…
We provide a natural generalization of a Riemannian structure, i.e., a metric, recently introduced by Sj\"{o}qvist for the space of non degenerate density matrices, to the degenerate case, i.e., the case in which the eigenspaces have…
Topological insulators and superconductors at finite temperature can be characterized by the topological Uhlmann phase. However, a direct experimental measurement of this invariant has remained elusive in condensed matter systems. Here, we…
The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are…
The realization of artificial gauge fields in ultracold atomic gases has opened up a path towards experimental studies of topological insulators and, as an ultimate goal, topological quantum matter in many-body systems. As an alternative to…
We study fermionic matrix product operator algebras and identify the associated algebraic data. Using this algebraic data we construct fermionic tensor network states in two dimensions that have non-trivial symmetry-protected or intrinsic…
A system with equal number of positive and negative charges confined in a box with a small but finite thickness is modeled as a function of temperature using mesoscale numerical simulations, for various values of the charges. The Coulomb…
We show that topological characterization and classification in $D$-dimensional systems, which are thermodynamically large in only $D-\delta$ dimensions and finite in size in $\delta$ dimensions, is fundamentally different from that of…
We discuss the topological phase transition of the spin-$\frac{1}{2}$ fermionic Haldane model with repulsive on-site interaction. We show that the Berry curvature of the topological Hamiltonian, the first Chern number, and the topological…
Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated…
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds…
We review the dimensional reduction procedure in the group cohomology classification of bosonic SPT phases with finite abelian unitary symmetry group. We then extend this to include general reductions of arbitrary dimensions and also extend…
In recent experiments with ultracold atoms, both two-dimensional (2d) Chern insulators and one-dimensional (1d) topological charge pumps have been realized. Without interactions, both systems can be described by the same Hamiltonian, when…
We investigate the harmonically trapped 2D fermionic systems with a effective spin-orbit coupling and intrinsic s-wave superfluidity under the local density approximation, and find that there is a critical value for Zeeman field. When the…
Higher-dimensional topological phases play a key role in understanding the lower-dimensional topological phases and the related topological responses through a dimensional reduction procedure. In this work, we present a Dirac-type model of…
In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using field…
Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local-global correspondence between the…
We present models of topological insulating Hamiltonians exhibiting intrinsic altermagnetic features, protected by combined three-fold or four-fold rotational symmetries with time-reversal. We demonstrate that the spin Chern number serves…