Using a Tower of States to Model the Two-Nucleon Interaction

A. Johnson

Jiajie Shen, Hui Jiang, G. J. Fu

We investigate the robustness of ``noncollective'' rotational behavior for nuclei with random two-body interactions in the framework of nuclear shell model. The normal $I(I+1)$ behavior of average excitation energy of yrast states is universal for both even-nucleon and odd-nucleon systems by two-body random ensemble. In some special random samplings, especially the samplings with spin-${I}_{\mathrm{max}}$ ground state, the inverse noncollective rotational behavior is found for both even-nucleon and odd-nucleon systems in this paper. Interestingly, above rotational behaviors are still robust in the presence of random two-body interactions plus realistic single-particle energies.

Jingya Wang, Zenan Liu, Bin-Bin Mao +4 more

Based on the study of a one-dimensional (1D) antiferromagnetic Heisenberg model on a comb lattice, this work identifies an example of spontaneous continuous symmetry breaking in a 1D system with short-range interactions. When a symmetry-preserving relevant perturbation is applied to the system, we find that this model can always be described by the Marshall-Lieb-Mattis (MLM) theorem. The Shen-Qiu-Tian theorem establishes a direct connection between the MLM theorem (in the case of bipartite lattices with unequal numbers of sites in the two sublattices) and the breaking of continuous symmetry. Moreover, although authors of previous studies have suggested that the presence of a tower of states (TOS) serves as an important numerical diagnostic of the tendency of a system toward spontaneous symmetry breaking, these investigations have primarily focused on two-dimensional systems. In 1D systems, however, the presence of long-range order does not automatically imply the emergence of a TOS. Here, we observe the existence of a TOS in a 1D realistic ferrimagnetic lattice system with short-range interactions.

Joseph Polchinski, Vladimir Rosenhaus

The SYK model consists of N ≫ 1 fermions in 0 + 1 dimensions with a random, all-to-all quartic interaction. Recently, Kitaev has found that the SYK model is maximally chaotic and has proposed it as a model of holography. We solve the SchwingerDyson equation and compute the spectrum of two-particle states in SYK, finding both a continuous and discrete tower. The four-point function is expressed as a sum over the spectrum. The sum over the discrete tower is evaluated.