Related papers: Exactly Solvable Hamiltonian for Non-Abelian Quasi…

The t-J model in the spinless-fermion representation is studied. An effective Hamiltonian for the quasiparticles is derived using canonical transformation approach. It is shown that the rather simple form of the transformation generator…

A recent thermal Hall conductance experiment [Banerjee et al., Nature {\bf559}, 205 (2018)] for $\nu = 5/2$ fractional quantum Hall system appears to rule out both the Pfaffian and anti-Pfaffian and be in favor of the PH-Pfaffian…

In a Laughlin fractional quantum Hall state, one- and two-quasihole states can be obtained by diagonalizing the many-body Hamiltonian with a trapping potential or, for larger systems, from the linear combination of the edge Jack…

We present a detailed analysis of the exact numerical spectrum of up to ten interacting electrons in the first Landau level on the disk geometry. We study the edge excitations of the hierarchical plateaus and check the predictions of two…

We develop a formalism to describe quasihole condensates in quantum Hall liquids and thereby extend the conformal field theory approach to the full hierarchy of spin-polarized Abelian states, and to several classes of non-Abelian…

The fractional quantum Hall (FQH) effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most FQH studies have focused on the lowest Landau level (LL), whose fractional states are…

Using a new class of exactly solvable models based on the pairing interaction, we show that it is possible to construct integrable Hamiltonians with a Wigner distribution of nearest neighbor level spacings. However, these Hamiltonians…

The $k$-local Hamiltonian problem is a central model for quantum many-body systems and Hamiltonian complexity. Semidefinite programming and noncommutative sum-of-squares hierarchies provide systematic certificates for ground-state energies,…

The abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-abelian states emanating from the {\nu} = 5/2 Moore-Read state in the second Landau…

We introduce and study a disorder-free version of the quantum breakdown model with all-to-all interactions. The Hamiltonian factorizes into the product of the zero-momentum-mode occupation number and a quadratic Hamiltonian including only…

A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wavefunction for two electrons occupying the same Wannier orbital…

Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving…

Several explicit examples of quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known…

Realizing topological flat bands with tailored single-particle Hilbert spaces is a critical step toward exploring many-body phases, such as those featuring anyonic excitations. One prominent example is the Kapit-Mueller model, a variant of…

We analyze tunneling of non-Abelian quasiparticles between the edges of a quantum Hall droplet at Landau level filling fraction nu=5/2, assuming that the electrons in the first excited Landau level organize themselves in the non-Abelian…

Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter physics, nuclear physics, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is…

We present analytic expressions for the exact density functional and Kohn-Sham Hamiltonian of simple tight-binding models of correlated electrons. These are the single- and double-site versions of the Anderson, Hubbard and spinless fermion…

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 show that minimal-surface non-Euclidean elastic plates share the same low-energy effective theory as Haldane's dimerized quantum spin chain. As a result, such elastic plates support fractional excitations, which take the form of…

This paper is devoted to the construction of what we will call {\em exactly solvable models}, i.e. of quantum mechanical systems described by an Hamiltonian $H$ whose eigenvalues and eigenvectors can be explicitly constructed out of some…