Related papers: Random loop representations for quantum spin syste…
We review the random loop representations of Toth and Aizenman-Nachtergaele for quantum Heisenberg models. They can be combined and extended so as to include the quantum XY model and certain SU(2)-invariant spin 1 systems. We explain the…
We review random loop representations for the spin-1/2 quantum Heisenberg models, that are due to Toth (ferromagnet) and Aizenman-Nachtergaele (antiferromagnet). These representations can be extended to models that interpolate between the…
A quantum computing circuit is presented that approximates a single spin wave quantum on a linear chain of spin 1/2 particles described by a Heisenberg Hamiltonian. The circuit is a product state where each qubit represents a spin. The spin…
We consider a family of quantum loop models in 2+1 spacetime dimensions with marginally long-ranged and statistical interactions mediated by a U$(1)$ gauge field, both purely in 2+1 dimensions and on a surface in a 3+1 dimensional bulk…
A quantum spin-$\frac{1}{2}$ chain with an axial symmetry is normally described by quasiparticles associated with the spins oriented along the axis of rotation. Kinetic constraints can enrich such a description by setting apart different…
These notes give a mathematical introduction to two seemingly unrelated topics: (i) quantum spin systems and their cycle and loop representations, due to T\'oth and Aizenman-Nachtergaele; (ii) coagulation-fragmentation stochastic processes.…
We present a systematic analysis of quantum Heisenberg-, XY- and interchange models on the complete graph. These models exhibit phase transitions accompanied by spontaneous symmetry breaking, which we study by calculating the generating…
We consider the general spin-1 SU(2) invariant Heisenberg model with a two-body interaction. A random loop model is introduced and relations to quantum spin systems is proved. Using this relation it is shown that for dimensions 3 and above…
Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time…
The emergence of a collective behavior in a many-body system is responsible of the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different…
While classical spin systems in random networks have been intensively studied, much less is known about quantum magnets in random graphs. Here, we investigate interacting quantum spins on small-world networks, building on mean-field theory…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
The characterization of quantum magnetism in a large spin ($\geq 1$) system naturally involves both spin-vectors and -tensors. While certain types of spin-vector (e.g., ferromagnetic, spiral) and spin-tensor (e.g., nematic in frustrated…
Effects of randomness on the spin-1/2 and 1 antiferromagnetic Heisenberg chains are studied using the quantum Monte Carlo method with the continuous-time loop algorithm. We precisely calculated the uniform susceptibility, string order…
Quantum Heisenberg spin chains with random couplings and spin sizes are studied using a real-space renormalization group technique. These systems belong to a new universality class of disordered quantum spin systems realized in {\it e.g.}…
The rounding of first order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a $d$-dimensional…
A semiclassical theory of a quantum spin$-S$ model with competing ring and Heisenberg exchange terms on the triangular lattice is obtained. A mechanism for the generation of $Z_2$ vortices is exhibited. The vortices are shown to carry a…
Many statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and…
We consider a quantum many-body system made of $N$ interacting $S{=}1/2$ spins on a lattice, and develop a formalism which allows to extract, out of conventional magnetic observables, the quantum probabilities for any selected spin pair to…
We report on the emergence of a highly non-classical collective behavior in quantum parametric oscillators, which we name quantum hyperspin, induced by a tailored nonlinear interaction. This is the second quantized version of classical…