Related papers: Zero modes, Bosonization and Topological Quantum O…
We consider lattice Hamiltonians that arise from putting Haldane pseudopotentials into a second quantized or "guiding-center-only" form. These are fascinating examples for frustration free lattice Hamiltonians. This is so since even though…
We give a recursion relation for the second-quantized fermionic (bosonic) Halperin state, which avoids exact diagonalization of its two-component first-quantized parent Hamiltonian. We validate this formula by proving that the…
A subtle relation between Quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest…
We investigate lattice effects on wave functions that are lattice analogues of bosonic and fermionic Laughlin wave functions with number of particles per flux $\nu=1/q$ in the Landau levels. These wave functions are defined analytically on…
The fractional quantum Hall (FQH) effect is one of the most striking phenomena in condensed matter physics. It is described by a simple Laughlin wavefunction and has been thoroughly studied both theoretically and experimentally. In lattice…
We study lattice wave functions obtained from the SU(2)$_1$ Wess-Zumino-Witten conformal field theory. Following Moore and Read's construction, the Kalmeyer-Laughlin fractional quantum Hall state is defined as a correlation function of…
We analyze a set of models frequently appearing in quantum optical settings by expressing their Hamiltonians in terms of Fock-state lattices. The few degrees-of-freedom of such models, together with the system symmetries, make the emerging…
Model wave functions are essential for studying fractional quantum Hall phases, yet lattice model states have so far been limited to bosonic systems with on-site interactions. In this work, by combining analytical and numerical methods, we…
We introduce one-dimensional lattice models with exact matrix-product ground states describing the fractional quantum Hall (FQH) states in Laughlin series (given by filling factors $\nu=1/q$) on torus geometry. Surprisingly, the exactly…
We construct a recursive second-quantized formula for Moore-Read Pfaffian states. We demonstrate the utility of such second-quantized presentations by directly proving the existence of frustration-free parent Hamiltonians, without appealing…
We numerically study the behavior of spin--$1/2$ fermions on a two-dimensional square lattice subject to a uniform magnetic field, where opposite spins interact via an on-site attractive interaction. Starting from the non-interacting case…
A system of two identical spinless bosons on the two-dimensional lattice is considered under the assumption that on-site and first and second nearest-neighboring site interactions between the bosons are only nontrivial and that these…
Recently, it was shown that fractional quantum Hall states can be defined on fractal lattices. Proposed exact parent Hamiltonians for these states are nonlocal and contain three-site terms. In this work, we look for simpler, approximate…
We study the Bisognano-Wichmann Hamiltonian for fractional quantum Hall states defined on a sphere and explore its relationship with the entanglement Hamiltonian associated to the state. We present results for several examples, namely the…
Conformal field theory has turned out to be a powerful tool to derive interesting lattice models with analytical ground states. Here, we investigate a class of critical, one-dimensional lattice models of fermions and hardcore bosons related…
We analyze general zero mode properties of the parent Hamiltonian of the unprojected Jain-2/5 state. We characterize the zero mode condition associated to this Hamiltonian via projection onto a four-dimensional two-particle subspace for…
There has been a significant interest in the last years in finding fractional quantum Hall physics in lattice models, but it is not always clear how these models connect to the corresponding models in continuum systems. Here we introduce a…
The combination of interactions and static gauge fields plays a pivotal role in our understanding of strongly-correlated quantum matter. Cold atomic gases endowed with a synthetic dimension are emerging as an ideal platform to…
We develop recursion relations, in particle number, for all (unprojected) Jain composite fermion (CF) wave functions. These recursions generalize a similar recursion originally written down by Read for Laughlin states, in mixed first-second…
Given a microscopic lattice Hamiltonian for a topologically ordered phase, we describe a tensor network approach to characterize its emergent anyon model and, in a chiral phase, also its gapless edge theory. First, a tensor network…