Mapping between the Heisenberg XX Spin Chain and Low-Energy QCD

Low Energy Properties of the Random Spin-1/2 Ferromagnetic-Antiferromagnetic Heisenberg Chain

The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet ph...

Diverging Heisenberg spin ladders: ground state and low energy excitations.

We consider a two-leg ladder system with interactions varying from constant rung coupling to systematic diminishing of rung interactions leading to diverging chains. We compare and contrast their ground state and excitation characteristics using density matrix renormalization group methods. We find that the finite spin gap in a constant coupling ladder develops into a gapless excitation with sl...

Critical exponents of the Heisenberg spin chain.

Inverse Participation Ratios in the Xx Spin Chain

We continue the study of the Inverse Participation Ratios (IPRs) of the XXZ Heisenberg spin chain initiated by Misguich, Pasquier and Luck (2016) by focusing on the case of the XX Heisenberg Spin Chain. For the ground state, Misguich et al. note that calculating the IPR is equivalent to Dyson’s constant term ex-conjecture. We express the IPRs of excited states as an apparently new “discrete” Ha...

First order quantum phase transitions in the XX spin chain

Quantum phase transitional behavior of a finite periodic XX spin1 2 chain with nearest neighbor interaction in a uniform transverse field is studied based on the simple exact solutions. It is found that there are [N/2] quantum critical points in the ground state, where N is the periodic number of the system and [x] stands for the integer part of x, when the interaction strength and magnitude of...