Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Nonlinear Constraints from Non-Abelian Internal Symmetries

Turko, L

Published Dec 19, 2001• 1 citation
OpenAlex

Abstract

Symmetry invariant local interaction of a many body system leads to global constraints. We obtain explicit forms of the global macroscopic condition assuring that at the microscopic level the evolution respects the overall symmetry.

Related papers

Macroconstraints from Microsymmetries

L. Turko

The dynamics governing the evolution of a many body system is constrained by a nonabelian local symmetry. We obtain explicit forms of the global macroscopic condition assuring that at the microscopic level the evolution respects the overall symmetry constraint.

arXiv:hep-th/0010212•Oct 24, 2000•0 citations

Macroconstraints from Microsymmetries of Macrosystems

L. Turko, Johann Rafelski A

The dynamics governing the evolution of a many body system is constrained by a nonabelian local symmetry. We obtain a general form of the global macroscopic conditions assuring that at the microscopic level the evolution respects the overall symmetry constraint. These conditions does not depend on detailed dynamics of the system. It is shown that a nonabelian internal symmetry leads to the new subsidiary condition imposed on the system. A structure of constraints is analysed.

arXiv:nucl-th/0011047•Nov 13, 2000•2 citations

On Global and Nonlinear Symmetries in Quantum Mechanics

Heinz Dietrich Doebner

(3) and furthermore nonlinear Schroedinger equations with given potentials which were also derived in another context in [1, 2].

Acta Polytechnica•Jan 3, 2010•0 citations

Theory of quantum circuits with Abelian symmetries

Iman Marvian

Quantum circuits with gates (local unitaries) respecting a global symmetry have broad applications in quantum information science and related fields, such as condensed-matter theory and quantum thermodynamics. However, despite their widespread use, fundamental properties of such circuits are not well understood. Recently, it was found that generic unitaries respecting a global symmetry cannot be realized, even approximately, using gates that respect the same symmetry. This observation raises important open questions: What unitary transformations can be realized with k -local gates that respect a global symmetry? In other words, in the presence of a global symmetry, how does the locality of interactions constrain the possible time evolution of a composite system? In this work, we address these questions for the case of Abelian (commutative) symmetries and develop constructive methods for synthesizing circuits with such symmetries. Remarkably, as a corollary, we find that, while the locality of interactions still imposes additional constraints on realizable unitaries, certain restrictions observed in the case of non-Abelian symmetries do not apply to circuits with Abelian symmetries. For instance, in circuits with a general non-Abelian symmetry such as SU ( d ) , the unitary realized in a subspace with one irreducible representation (charge) of the symmetry dictates the realized unitaries in multiple other sectors with inequivalent representations of the symmetry. Furthermore, in certain sectors, rather than all unitaries respecting the symmetry, the realizable unitaries are the symplectic or orthogonal subgroups of this group. We prove that none of these restrictions appears in the case of Abelian symmetries. This result suggests that global non-Abelian symmetries may affect the thermalization of quantum systems in ways not possible under Abelian symmetries. Published by the American Physical Society 2024

arXiv:2302.12466•Physical Review Research•Dec 18, 2024•15 citations

Supernematic

Dan Mao, Eun-Ah Kim

Quantum theory of geometrically frustrated systems is usually approached as a gauge theory where the local conservation law becomes the Gauss law. Here we show that it can do something fundamentally different: enforce a global conserved quantity via a non-perturbative tiling invariant, rigorously linking microscopic geometry to a new macroscopically phase-coherent state. In a frustrated bosonic model on the honeycomb lattice in the cluster-charging regime at fractional filling, this mechanism protects a conserved global quantum number, the sublattice polarization $\tilde{N} = N_A - N_B$. Quantum fluctuation drives the spontaneous symmetry breaking of this global U(1) symmetry to result in a supernematic (SN) phase -- an incompressible yet phase-coherent quantum state that breaks rotational symmetry without forming a superfluid or realizing topological order. This establishes a route to a novel quantum many-body state driven by combinatorial constraints.

cond-mat.str-elCross-listedarXiv:2511.10642•Nov 14, 2025•0 citations

The Role of Space Group Symmetries in Many Body Interacting Systems

Rahul Roy

Bulletin of the American Physical Society•Mar 6, 2014•0 citations
Quantum circuits with gates (local unitaries) respecting a global symmetry have broad applications in quantum information science and related fields, such as condensed-matter theory and quantum thermodynamics. However, despite their widespread use, fundamental properties of such circuits are not well understood. Recently, it was found that generic unitaries respecting a global symmetry cannot be realized, even approximately, using gates that respect the same symmetry. This observation raises important open questions: What unitary transformations can be realized with k -local gates that respect a global symmetry? In other words, in the presence of a global symmetry, how does the locality of interactions constrain the possible time evolution of a composite system? In this work, we address these questions for the case of Abelian (commutative) symmetries and develop constructive methods for synthesizing circuits with such symmetries. Remarkably, as a corollary, we find that, while the locality of interactions still imposes additional constraints on realizable unitaries, certain restrictions observed in the case of non-Abelian symmetries do not apply to circuits with Abelian symmetries. For instance, in circuits with a general non-Abelian symmetry such as SU ( d ) , the unitary realized in a subspace with one irreducible representation (charge) of the symmetry dictates the realized unitaries in multiple other sectors with inequivalent representations of the symmetry. Furthermore, in certain sectors, rather than all unitaries respecting the symmetry, the realizable unitaries are the symplectic or orthogonal subgroups of this group. We prove that none of these restrictions appears in the case of Abelian symmetries. This result suggests that global non-Abelian symmetries may affect the thermalization of quantum systems in ways not possible under Abelian symmetries. Published by the American Physical Society 2024
Quantum theory of geometrically frustrated systems is usually approached as a gauge theory where the local conservation law becomes the Gauss law. Here we show that it can do something fundamentally different: enforce a global conserved quantity via a non-perturbative tiling invariant, rigorously linking microscopic geometry to a new macroscopically phase-coherent state. In a frustrated bosonic model on the honeycomb lattice in the cluster-charging regime at fractional filling, this mechanism protects a conserved global quantum number, the sublattice polarization N~=NA−NB\tilde{N} = N_A - N_BN~=NA​−NB​. Quantum fluctuation drives the spontaneous symmetry breaking of this global U(1) symmetry to result in a supernematic (SN) phase -- an incompressible yet phase-coherent quantum state that breaks rotational symmetry without forming a superfluid or realizing topological order. This establishes a route to a novel quantum many-body state driven by combinatorial constraints.