We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev model. These are quantum mechanical models involving $N$ Majorana fermions. The supercharge is given by a polynomial expression in terms of the Majorana fermions with random coefficients. The Hamiltonian is the square of the supercharge. The ${\cal N}=1$ model with a single supercharge has unbroken supersymmetry at large $N$ , but non-perturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large $N$ equation, and also by performing numerical computations for small values of $N$ . We also compute the large $N$ spectrum of "singlet" operators, where we find a structure qualitatively similar to the ordinary SYK model. We also discuss an ${\cal N}=2$ version. In this case, the model preserves supersymmetry in the exact theory and we can compute a suitably weighted Witten index to count the number of ground states, which agrees with the large $N$ computation of the entropy. In both cases, we discuss the supersymmetric generalizations of the Schwarzian action which give the dominant effects at low energies.We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev model. These are quantum mechanical models involving $N$ Majorana fermions. The supercharge is given by a polynomial expression in terms of the Majorana fermions with random coefficients. The Hamiltonian is the square of the supercharge. The ${\cal N}=1$ model with a single supercharge has unbroken supersymmetry at large $N$, but non-perturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large $N$ equation, and also by performing numerical computations for small values of $N$. We also compute the large $N$ spectrum of "singlet" operators, where we find a structure qualitatively similar to the ordinary SYK model. We also discuss an ${\cal N}=2$ version. In this case, the model preserves supersymmetry in the exact theory and we can compute a suitably weighted Witten index to count the number of ground states, which agrees with the large $N$ computation of the entropy. In both cases, we discuss the supersymmetric generalizations of the Schwarzian action which give the dominant effects at low energies.

arXiv:1610.08917Physical review. D/Physical review. D.Mar 23, 201744 citations

Dynamical properties of the one-dimensional supersymmetric t-J model

Yasuhiro Saiga, Shinji Watanabe, Mitsuhiro Arikawa +5 more

Jan 1, 19990 citations

Some remarks on scattering theory in supersymmetric quantum systems

Asao Arai

First it is shown in an abstract mathematical framework of supersymmetric quantum theory that, under some conditions for the perturbation, the wave and the scattering operators on bosonic states have some connections with those on fermionic ones. In particular, a unitary equivalence between the two scattering operators is proved. Then, a class of supersymmetric quantum mechanical models on Rn is discussed and the abstract general results are applied to obtain some more explicit results on the supersymmetric potential scattering.First it is shown in an abstract mathematical framework of supersymmetric quantum theory that, under some conditions for the perturbation, the wave and the scattering operators on bosonic states have some connections with those on fermionic ones. In particular, a unitary equivalence between the two scattering operators is proved. Then, a class of supersymmetric quantum mechanical models on Rn is discussed and the abstract general results are applied to obtain some more explicit results on the supersymmetric potential scattering.

Journal of Mathematical PhysicsFeb 1, 198717 citations

Electron Addition Spectrum in the Supersymmetric t−J Model with Inverse-Square Interaction

Mitsuhiro Arikawa, Yasuhiro Saiga, Yoshio Kuramoto

The electron addition spectrum A+(k,omega) is obtained analytically for the one-dimensional (1D) supersymmetric t-J model with 1/r2 interaction. The result is obtained first for a small-sized system and its validity is checked against the numerical calculation. Then the general expression is found which is valid for arbitrary size of the system. The thermodynamic limit of A+(k,omega) has a simple analytic form with contributions from one spinon, one holon, and one antiholon-all of which obey fractional statistics. The upper edge of A+(k,omega) in the (k,omega) plane includes a delta-function peak which reduces to that of the single-electron band in the low-density limit.The electron addition spectrum A+(k,omega) is obtained analytically for the one-dimensional (1D) supersymmetric t-J model with 1/r2 interaction. The result is obtained first for a small-sized system and its validity is checked against the numerical calculation. Then the general expression is found which is valid for arbitrary size of the system. The thermodynamic limit of A+(k,omega) has a simple analytic form with contributions from one spinon, one holon, and one antiholon-all of which obey fractional statistics. The upper edge of A+(k,omega) in the (k,omega) plane includes a delta-function peak which reduces to that of the single-electron band in the low-density limit.

arXiv:cond-mat/0102333Physical Review LettersApr 2, 200132 citations

Generalizations of the Supersymmetric t-J Model

Holger Frahm, Markus P. Pfannmüller

Journal of Mathematical SciencesApr 1, 20010 citations

We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev model. These are quantum mechanical models involving

N

Majorana fermions. The supercharge is given by a polynomial expression in terms of the Majorana fermions with random coefficients. The Hamiltonian is the square of the supercharge. The

{\cal N}=1

model with a single supercharge has unbroken supersymmetry at large

N

, but non-perturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large

N

equation, and also by performing numerical computations for small values of

N

. We also compute the large

N

spectrum of "singlet" operators, where we find a structure qualitatively similar to the ordinary SYK model. We also discuss an

{\cal N}=2

version. In this case, the model preserves supersymmetry in the exact theory and we can compute a suitably weighted Witten index to count the number of ground states, which agrees with the large

N

computation of the entropy. In both cases, we discuss the supersymmetric generalizations of the Schwarzian action which give the dominant effects at low energies.