Related papers: Counting Trees in Supersymmetric Quantum Mechanics
We study the growth of the ground state degeneracy in the Kronecker model of quiver quantum mechanics. This is the simplest quiver with two gauge groups and bifundamental matter fields, and appears universally in the context of BPS state…
We investigate the ground states of classical Heisenberg spin systems which have point group symmetry. Examples are the regular polygons (spin rings) and the seven quasi-regular polyhedra including the five Platonic solids. For these…
To set up a self-consistent quantum field theory of degenerate systems, the unperturbed state should be described by a density matrix instead of a pure state. This increases the combinatorial complexity of the many-body equations. Hopf…
We propose a protocol to generate an antiferromagnetic S=1/2 Heisenberg model with the exact ground state based on a tree graph. The generated model has a correspondence with a tree graph and possesses the product state of singlet dimers as…
Combining the MPS degeneration formula for the Poincar\'e polynomial of moduli spaces of stable quiver representations and localization theory, it turns that the determination of the Euler characteristic of these moduli spaces reduces to a…
Solving ground states of quantum many-body systems has been a long-standing problem in condensed matter physics. Here, we propose a new unsupervised machine learning algorithm to find the ground state of a general quantum many-body system…
Two pictures of BPS bound states in Calabi-Yau compactifications of type II string theory exist, one as a set of particles at equilibrium separations from each other, the other as a fusion of D-branes at a single point of space. We show how…
We present a new method to study the ground state of quantum spin systems using the Monte Carlo techniques together with restructured intermediate states which we proposed previously. Our basic idea is to obtain coefficients in the…
Subsystem symmetries are intermediate between global and gauge symmetries. One can treat these symmetries either like global symmetries that act on subregions of a system, or gauge symmetries that act on the regions transverse to the…
Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can…
We solve $\mathcal{N}=1$ supersymmetric $A_{2}$ type $U(N)\times U(N)$ matrix models obtained by deforming $\mathcal{N}=2$ with symmetric tree level superpotentials of any degree exactly in the planar limit. These theories can be…
We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary rank in the $n$-dimensional Euclidean space as a linear combination of products of Kronecker deltas. By making full use of the symmetries, one…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group…
We give a geometric interpretation for superconformal quantum mechanics defined on a hyper-Kahler cone which has an equivariant symplectic resolution. BPS states are identified with certain twisted Dolbeault cohomology classes on the…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
This paper explores the use of a deformation by a root of unity as a tool to build models with a finite number of states for applications to quantum gravity. The initial motivation for this work was cosmological breaking of supersymmetry.…
The determination of ground state properties of quantum systems is a fundamental problem in physics and chemistry, and is considered a key application of quantum computers. A common approach is to prepare a trial ground state on the quantum…
Quantum simulations constructing probability tensors of biological multi-taxa in phylogenetic trees are proposed, in terms of positive trace preserving maps, describing evolving systems of quantum walks with multiple walkers. Basic…
A simple, general and practically exact method is developed to calculate the ground states of 1D macroscopic quantum systems with translational symmetry. Applied to the Hubbard model, a modest calculation reproduces the Bethe Ansatz…