Related papers: The $A_m^{(1)}$ Q-system
We show that real polarization method can be effectively used to geometrically quantize physical systems with compact phase space, like the spin. Our method enables us to construct a wave function of a qubit in both position and momentum…
We describe and discuss a solid state proposal for quantum computation with mobile spin qubits in one-dimensional systems, based on recent advances in spintronics. Static electric fields are used to implement a universal set of quantum…
Some recent developments in the theory of quantum spin systems are reviewed.
It is suggested to map the qubits into solid state NMR spin system collective states instead of the states of the individual spin. Such an approach introduces the stable computational basis without any additional actions and allows to…
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…
For a (classically) integrable quantum mechanical system with two degrees of freedom, the functional dependence $\hat{H}=H_Q(\hat{J}_1,\hat{J}_2)$ of the Hamiltonian operator on the action operators is analyzed and compared with the…
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wavefunctions that are relevant in the behavior of the system under study. Hamiltonian symmetries are an important…
A detailed construction of the universal integrability objects related to the integrable systems associated with the quantum group $\mathrm U_q(\mathcal L(\mathfrak{sl}_2))$ is given. The full proof of the functional relations in the form…
We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded…
In the framework of 't Hooft's quantization proposal, we show how to obtain from the composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be interpreted…
We define a $q$-deformation of the classical ring of integer-valued polynomials which we call the ring of quantum integer-valued polynomials. We show that this ring has a remarkable combinatorial structure and enjoys many positivity…
For the quantum integer $[n]_q = 1+q+...+q^{n-1}$ there is a natural polynomial multiplication $*_q$ such that $[m]_q *_q [n]_q = [mn]_q$. This multiplication leads to the functional equation $f_{mn}(q) = f_m(q)f_n(q^m),$ defined on a given…
A general and computable criterion for k-(in)separability in continuous multipartite quantum systems is presented. The criterion can be experimentally implemented with a finite and comparatively low number of local observables. We discuss…
An integral transform for G=U(1,q) is studied. The transform maps the positive spin ladder representations of G on a Bargmann-Segal-Fock space F_n^1,q into a space of polynomial-valued functions on the bounded realization B^q of G/K. An…
We formulate a theory of invariants for the spin symmetric group in some suitable modules which involve the polynomial and exterior algebras. We solve the corresponding graded multiplicity problem in terms of specializations of the Schur…
We calculate the correlation functions of strings of spin operators for integrable quantum circuits exactly. These observables can be used for calibration of quantum simulation platforms. We use algebraic Bethe Ansatz, in combination with…
We rewrite the 1+1 Causal Dynamical Triangulations model as a spin system and thus provide a new method of solution of the model.
A method is proposed for obtaining a systematic expansion of thermodynamic functions of spin systems with large spin S in powers of 1/S. It uses the cumulant technique and a coherent-state representation of the partition function Z. The…
We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear sigma-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and…
We review the recent progress in formulating a quantum kinetic theory for the polarization of spin-$\frac{1}{2}$ massive quarks from the leading-log order of perturbative QCD.