Related papers: Spin(9) Average of SU(N) Matrix Models I. Hamilton…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
General aspects of higher-spin gauge theory and unfolded formulation are briefly recalled with some emphasize on the recent results on the breaking of $sp(8)$ symmetry by current interactions and construction of invariant functionals…
We discuss the relation between ensemble and time averages for quasistationary states of low-dimensional symplectic maps that present remarkable analogies with similar states detected in many-body long-range-interacting Hamiltonian systems.
We focus on symmetries related to matrices and vectors appearing in the simulation of quantum many-body systems. Spin Hamiltonians have special matrix-symmetry properties such as persymmetry. Furthermore, the systems may exhibit physical…
We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the…
We provide a systematic treatment of the tenfold way of classifying fermionic systems that naturally allows for the study of those with arbitrary $N$-body interactions. We identify four types of symmetries that such systems can possess,…
We consider free and proper cotangent-lifted symmetries of Hamiltonian systems. For the special case of G = SO(3), we construct symplectic slice coordinates around an arbitrary point. We thus obtain a parametrisation of the phase space…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
We propose a generalization of the supersymmetric representation of spins with symplectic symmetry, generalizing the rotation group of the spin from SU(2) to SP(N). As a test application of this new representation, we consider two toy…
Mean-field models of 2-spin Ising spin glasses with interaction matrices taken from ensembles which are invariant under O(N) transformations are studied. A general study shows that the nature of the spin glass transition can be deduced from…
To study exotic excitations described by parafermions in the possible spin liquid states of SU($n$) spin systems, we introduce a parafermion parton approach. The SU($n$) spin operators can be represented by clock and shift matrices, which…
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…
We develop new tools in the theory of nonlinear random matrices and apply them to study the performance of the Sum of Squares (SoS) hierarchy on average-case problems. The SoS hierarchy is a powerful optimization technique that has achieved…
We construct lists of supersymmetric models with extended gauge groups at intermediate steps, all of which are based on SO(10) unification. We consider three different kinds of setups: (i) The model has exactly one additional intermediate…
The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition…
We give a method for computing the ensemble average of multiplicative class functions over the Gaussian ensemble of real asymmetric matrices. These averages are expressed in terms of the Pfaffian of Gram-like antisymmetric matrices formed…
In seven dimensions any spin manifold admits an SU(2) structure and therefore very general M-theory compactifications have the potential to allow for a reduction to N=4 gauged supergravity. We perform this general SU(2) reduction and give…
The pseudo-SU(3) model is extended to explicitly include the spin and proton-neutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The…
Motivated by group-theoretical questions that arise in the context of asymptotic symmetries in gravity, we study model spaces and their quantization from the viewpoint of constrained Hamiltonian systems. More precisely, we propose that a…
We show that the requirement of $S_3\times Spin(d)$ invariance for a ``asymptotically free'' SU(3)-Cartan subalgebra wave-function does {\em not} give a unique candidate for a SU(3)-invariant zero energy state of the d=9 supersymmetric…