T − W relation and free energy of the Heisenberg chain at a finite temperature

A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t − W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corre- sponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.

$$\rho $$–Meson Form-factors in Point form of Poincaré-Invariant Quantum Mechanics

Form-factors investigation of $$\rho ^{\pm }$$ ρ ± –mesons was carried out within the framework of the relativistic quark model, based on point form of Poincaré-invariant quantum mechanics taking into account the internal structure of constituent quarks. It is shown that the parameters of the model obtained from the condition of the agreement of theoretical calculations with experimental data on leptonic decays for light $$\pi ^{\pm }$$ π ± — and $$\rho ^{\pm }$$ ρ ± –mesons lead to the results correlating with calculations in models based on light-front and instant forms of dynamics. The proposed scheme for the combined description of lepton transitions of pseudoscalar and vector mesons that is based on point form of dynamics, leads to the results on the magnetic moment of $$\rho ^{\pm }$$ ρ ± –meson correlating with the experimental data and other models.

Parallel quantum simulation of large systems on small NISQ computers

Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translates infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution of arbitrary one-dimensional systems. The illustrative simulated output of these codes for achievable circuit sizes is given.

Invariant Quantum States of Quadratic Hamiltonians

The problem of finding covariance matrices that remain constant in time for arbitrary multi-dimensional quadratic Hamiltonians (including those with time-dependent coefficients) is considered. General solutions are obtained.

Self-dual $S_3$-invariant quantum chains

We investigate the self-dual three-state quantum chain with nearest-neighbor interactions and S_3S3, time-reversal, and parity symmetries. We find a rich phase diagram including gapped phases with order-disorder coexistence, integrable critical points with U(1)U(1) symmetry, and ferromagnetic and antiferromagnetic critical regions described by three-state Potts and free-boson conformal field theories respectively. We also find an unusual critical phase which appears to be described by combining two conformal field theories with distinct “Fermi velocities”. The order-disorder coexistence phase has an emergent fractional supersymmetry, and we find lattice analogs of its generators.