skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Composing arbitrarily many SU(N) fundamentals
We compute the multiplicity of the irreducible representations in the decomposition of the tensor product of an arbitrary number n of fundamental representations of SU(N), and we identify a duality in the representation content of this decomposition. Our method utilizes the mapping of the representations of SU(N) to the states of free fermions on the circle, and can be viewed as a random walk on a multidimensional lattice. We also derive the large-n limit and the response of the system to an external non-abelian magnetic field. These results can be used to study the phase properties of non-abelian ferromagnets and to take various scaling limits.  more » « less
Award ID(s):
2112729
PAR ID:
10532729
Author(s) / Creator(s):
;
Publisher / Repository:
Nuclear Physics B
Date Published:
Journal Name:
Nuclear Physics B
Volume:
994
Issue:
C
ISSN:
0550-3213
Page Range / eLocation ID:
116314
Subject(s) / Keyword(s):
SU(N), representation, composition, matrix models, non-abelian
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; (, Nuclear Physics B)
    We study the thermodynamics of a non-abelian ferromagnet consisting of “atoms” each carrying a fun-damental representation of SU(N), coupled with long-range two-body quadratic interactions. We uncover a rich structure of phase transitions from non-magnetized, global SU(N)-invariant states to magnetized ones breaking global invariance to SU(N−1) ×U(1). Phases can coexist, one being stable and the other metastable, and the transition between states involves latent heat exchange, unlike in usual SU(2)ferro-magnets. Coupling the system to an external non-abelian magnetic field further enriches the phase structure, leading to additional phases. The system manifests hysteresis phenomena both in the magnetic field, as in usual ferromagnets, and in the temperature, in analogy to supercooled water. Potential applications are in fundamental situations or as a phenomenological model. 
    more » « less
  2. (, Physical Review Research)
    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 Society2024 
    more » « less
  3. ; ; (, SciPost Physics)
    We introduce a mathematical framework for symmetry-resolved entanglement entropy with a non-Abelian symmetry group. To obtain a reduced density matrix that is block-diagonal in the non-Abelian charges, we define subsystems operationally in terms of subalgebras of invariant observables. We derive exact formulas for the average and the variance of the typical entanglement entropy for the ensemble of random pure states with fixed non-Abelian charges. We focus on compact, semisimple Lie groups. We show that, compared to the Abelian case, new phenomena arise from the interplay of locality and non-Abelian symmetry, such as the asymmetry of the entanglement entropy under subsystem exchange, which we show in detail by computing the Page curve of a many-body system with SU(2) symmetry. 
    more » « less
  4. ; ; (, Physical Review A)
    We propose a practical protocol to generate and observe a non-Abelian geometric phase using a periodically driven Raman process in the hyperfine ground-state manifold of atoms in a dilute ultracold gas. Our analysis is based upon recent developments and application of Floquet theory to periodically driven quantum systems. The simulation results show the non-Abelian gauge transformation and the noncommuting property of the SU(2) transformation operators. Based on these results, we propose a possible experimental implementation with an ultracold dilute Bose gas. 
    more » « less
  5. ; ; ; ; ; (, Physical Review B)
    Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry's non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we identify a “spin-sharpening transition.” Across the transition, the rate at which measurements reveal information about the total spin quantum number changes parametrically with system size. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email