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

arXiv:0907.4360 · Physical Review B

Duality, quantum skyrmions, and the stability of a SO(3) two-dimensional quantum spin glass

C. M. S. da Conceição, Eduardo C. Marino

Published Aug 27, 2009• 3 citations
arXivHTMLPDF

Abstract

Quantum topological excitations (skyrmions) are analyzed from the point of view of their duality to spin excitations in the different phases of a disordered two-dimensional, short-range interacting, SO(3) quantum magnetic system of Heisenberg type. The phase diagram displays all the phases, which are allowed by the duality relation. We study the large-distance behavior of the two-point correlation function of quantum skyrmions in each of these phases and, out of this, extract information about the energy spectrum and nontriviality of these excitations. The skyrmion correlators present a power-law decay in the spin-glass (SG) phase, indicating that these quantum topological excitations are gapless but nontrivial in this phase. The SG phase is dual to the AF phase, in the sense that topological and spin excitations are, respectively, gapless in each of them. The Berezinskii-Kosterlitz-Thouless mechanism guarantees the survival of the SG phase at $T\ensuremath{\ne}0$, whereas the AF phase is washed out to $T=0$ by the quantum fluctuations. Our results suggest a more symmetric way of characterizing a SG phase: one for which both the order and disorder parameters vanish, namely, $⟨\ensuremath{\sigma}⟩=0$ and $⟨\ensuremath{\mu}⟩=0$, where $\ensuremath{\sigma}$ is the spin and $\ensuremath{\mu}$ is the topological excitation operators.

DOI
10.1103/physrevb.80.064422

Related papers

Quantum field theory solution for a short-range interacting SO ( 3 ) quantum spin-glass

C. M. S. da Conceição, Eduardo C. Marino

We study the quenched disordered magnetic system, which is obtained from the 2D SO(3) quantum Heisenberg model, on a square lattice, with nearest neighbors interaction, by taking a Gaussian random distribution of couplings centered in an antiferromagnetic coupling, J¯>0 and with a width ΔJ. Using coherent spin states we can integrate over the random variables and map the system onto a field theory, which is a generalization of the SO(3) nonlinear sigma model with different flavors corresponding to the replicas, coupling parameter proportional to J¯ and having a quartic spin interaction proportional to the disorder (ΔJ). After deriving the CP1 version of the system, we perform a calculation of the free energy density in the limit of zero replicas, which fully includes the quantum fluctuations of the CP1 fields zi. We, thereby obtain the phase diagram of the system in terms of (T,J¯,ΔJ). This presents an ordered antiferromagnetic (AF) phase, a paramagnetic (PM) phase and a spin-glass (SG) phase. A critical curve separating the PM and SG phases ends at a quantum critical point located between the AF and SG phases, at T=0. The Edwards–Anderson order parameter, as well as the magnetic susceptibilities are explicitly obtained in each of the three phases as a function of the three control parameters. The magnetic susceptibilities show a Curie-type behavior at high temperatures and exhibit a clear cusp, characteristic of the SG transition, at the transition line. The thermodynamic stability of the phases is investigated by a careful analysis of the Hessian matrix of the free energy. We show that all principal minors of the Hessian are positive in the limit of zero replicas, implying in particular that the SG phase is stable.

arXiv:0903.0305•Nuclear Physics B•Feb 26, 2009•5 citations

Phase diagram of a short-range interacting SO(3) quantum spin-glass

C. M. S. da Conceição, Eduardo C. Marino

We present a stable approximate solution for a quantum, short-range interacting, SO(3) Heisenberg disordered spin system on a square lattice, with a Gaussian distribution of couplings centered on an anti-ferromagnetic coupling . The phase diagram T × contains a Néel (AF) phase at T = 0, > 0 and a spin-glass (SG) phase below a critical line, namely, T < Tc( ), < 0 . The rest of the phase diagram is occupied by the paramagnetic (PM) phase.

Journal of Physics Conference Series•Jan 1, 2010•0 citations

Stable Mean-Field Solution of a Short-Range Interacting SO(3) Quantum Heisenberg Spin Glass

C. M. S. da Conceição, Eduardo C. Marino

We present a mean-field solution for a quantum, short-range interacting, disordered, SO(3) Heisenberg spin model, in which the Gaussian distribution of couplings is centered in an antiferromagnetic (AF) coupling J[over ]>0, and which, for weak disorder, can be treated as a perturbation of the pure AF Heisenberg system. The phase diagram contains, apart from a Néel phase at T=0, spin-glass and paramagnetic phases whose thermodynamic stability is demonstrated by an analysis of the Hessian matrix of the free-energy. The magnetic susceptibilities exhibit the typical cusp of a spin-glass transition.

arXiv:0802.0278•Physical Review Letters•Jul 14, 2008•7 citations

Quantum Spin Glass in the Two-Dimensional Disordered Heisenberg Model via Foundation Neural-Network Quantum States

Luciano Loris Viteritti, Riccardo Rende, Giacomo Bracci-Testasecca +4 more

We investigate the two-dimensional frustrated quantum Heisenberg model with bond disorder on nearest-neighbor couplings using the recently introduced Foundation Neural-Network Quantum States framework, which enables accurate and efficient computation of disorder-averaged observables with a single variational optimization. Simulations on large lattices reveal an extended region of the phase diagram where conventional magnetic long-range order vanishes in the thermodynamic limit, while the Edwards-Anderson order parameter remains finite, signaling the emergence of a quantum spin-glass phase. These findings, supported by a semiclassical analysis based on a large-spin expansion, provide compelling evidence that the spin glass-order is stable against quantum fluctuations, unlike the classical case where it disappears at any finite temperature.

arXiv:2507.05073•Jul 7, 2025•0 citations

Gapless bosonic excitation without symmetry breaking: An algebraic spin liquid with soft gravitons

Cenke Xu

A quantum ground state of matter is realized in a bosonic model on a three-dimensional fcc lattice with emergent low energy excitations. The phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the graviton, although they have a soft $\ensuremath{\omega}\ensuremath{\sim}{k}^{2}$ dispersion relation. There are three branches of gapless excitations in this phase, one of which is gapless scalar trace mode, the other two have the same polarization and gauge symmetries as the gravitons. The dynamics of this phase is described by a set of Maxwell's equations. The defects carrying gauge charges can drive the system into the superfluid order when the defects are condensed; also the topological defects are coupled to the dual gauge field in the same manner as the charge defects couple to the original gauge field, after the condensation of the topological defects, the system is driven into the Mott insulator phase. In the two-dimensional case, the gapless soft graviton as well as the algebraic liquid phase are destroyed by the vertex operators in the dual theory, and the stripe order is most likely to take place close to the two-dimensional quantum critical point at which the vertex operators are tuned to zero.

arXiv:cond-mat/0609595•Physical Review B•Dec 27, 2006•112 citations

Through the looking glass of unconventional topological phases and fractionalization

Flores Calderon, Rafael Alvaro

Ever since quantum mechanics and relativity appeared at the beginning of the 20th century, physics has been rocked to its foundations. Novel ideas and applications surged relentlessly from the minds of those brave enough to venture into the unknown new worlds revealed by the new sciences. This year marks the centenary of Heisenberg’s quantum mechanics, and the exploration has not waned; rather, the frontiers of our knowledge now extend beyond fundamental theories into the complex playground of symmetry, topology, and emergence. We are faced with the challenge of understanding and predicting the behavior of complex systems in which the interplay of all three is essential for explaining their unique phenomena. Amid such an insurmountable challenge, novel viewpoints and signatures can often guide us through this dense web of complexity. In this doctoral thesis, we explore distinct scenarios where the intertwining of symmetry and topology naturally leads to previously unexplored phenomena, and subtle signatures arise from the combination of old and new theoretical frameworks in the weak and strong coupling regimes. In part one, we study weakly interacting topological phases. In chapter 2, we introduce the idea of time-reversal invariant finite-size topology. We identify signatures of a higher-dimensional bulk topological phase within thin films and wires; we probe this via Wilson loop spectroscopy and electromagnetic responses. Chapter 3 deals with extending previously studied topological skyrmion phases to time-reversal invariant systems. A generalization of the time-reversal parity invariant corresponds to a bulk-boundary texture of the pseudo-spin degrees of freedom. Moreover, our skyrmion invariant is directly linked to a reduced entanglement spectrum with protected spectral flow. Part two of this thesis is dedicated to strongly interacting electrons, where the effective description is that of a network of spins displaying the unconventional physics of spin liquids. In chapter 4, we describe how fractionalization can be generalized in classical spin liquids to yield irrational magnetic moments of dilution clusters. These clusters act as gauge charges for the low-energy lattice gauge theory. Moreover, we show that for a higher-rank gauge theory, distinctive emergent non-decaying spin textures and interactions are hallmarks of the unusual topological magnet. Chapter 5 studies a fragile spin liquid in three dimensions, which displays fractionalization but no algebraically decaying correlations. We find that not only is the Heisenberg model disordered, but the Ising model is as well. Perturbing away, we find a special point where quantum fluctuations stabilize a Z_2 quantum spin liquid.

•Jan 1, 2025•0 citations
Quantum topological excitations (skyrmions) are analyzed from the point of view of their duality to spin excitations in the different phases of a disordered two-dimensional, short-range interacting, SO(3) quantum magnetic system of Heisenberg type. The phase diagram displays all the phases, which are allowed by the duality relation. We study the large-distance behavior of the two-point correlation function of quantum skyrmions in each of these phases and, out of this, extract information about the energy spectrum and nontriviality of these excitations. The skyrmion correlators present a power-law decay in the spin-glass (SG) phase, indicating that these quantum topological excitations are gapless but nontrivial in this phase. The SG phase is dual to the AF phase, in the sense that topological and spin excitations are, respectively, gapless in each of them. The Berezinskii-Kosterlitz-Thouless mechanism guarantees the survival of the SG phase at T\ensuremath≠0T\ensuremath{\ne}0T\ensuremath=0, whereas the AF phase is washed out to T=0T=0T=0 by the quantum fluctuations. Our results suggest a more symmetric way of characterizing a SG phase: one for which both the order and disorder parameters vanish, namely, ⟨\ensuremathσ⟩=0⟨\ensuremath{\sigma}⟩=0⟨\ensuremathσ⟩=0 and ⟨\ensuremathμ⟩=0⟨\ensuremath{\mu}⟩=0⟨\ensuremathμ⟩=0, where \ensuremathσ\ensuremath{\sigma}\ensuremathσ is the spin and \ensuremathμ\ensuremath{\mu}\ensuremathμ is the topological excitation operators.
We study the quenched disordered magnetic system, which is obtained from the 2D SO(3) quantum Heisenberg model, on a square lattice, with nearest neighbors interaction, by taking a Gaussian random distribution of couplings centered in an antiferromagnetic coupling, J¯>0 and with a width ΔJ. Using coherent spin states we can integrate over the random variables and map the system onto a field theory, which is a generalization of the SO(3) nonlinear sigma model with different flavors corresponding to the replicas, coupling parameter proportional to J¯ and having a quartic spin interaction proportional to the disorder (ΔJ). After deriving the CP1 version of the system, we perform a calculation of the free energy density in the limit of zero replicas, which fully includes the quantum fluctuations of the CP1 fields zi. We, thereby obtain the phase diagram of the system in terms of (T,J¯,ΔJ). This presents an ordered antiferromagnetic (AF) phase, a paramagnetic (PM) phase and a spin-glass (SG) phase. A critical curve separating the PM and SG phases ends at a quantum critical point located between the AF and SG phases, at T=0. The Edwards–Anderson order parameter, as well as the magnetic susceptibilities are explicitly obtained in each of the three phases as a function of the three control parameters. The magnetic susceptibilities show a Curie-type behavior at high temperatures and exhibit a clear cusp, characteristic of the SG transition, at the transition line. The thermodynamic stability of the phases is investigated by a careful analysis of the Hessian matrix of the free energy. We show that all principal minors of the Hessian are positive in the limit of zero replicas, implying in particular that the SG phase is stable.
We present a mean-field solution for a quantum, short-range interacting, disordered, SO(3) Heisenberg spin model, in which the Gaussian distribution of couplings is centered in an antiferromagnetic (AF) coupling J[over ]>0, and which, for weak disorder, can be treated as a perturbation of the pure AF Heisenberg system. The phase diagram contains, apart from a Néel phase at T=0, spin-glass and paramagnetic phases whose thermodynamic stability is demonstrated by an analysis of the Hessian matrix of the free-energy. The magnetic susceptibilities exhibit the typical cusp of a spin-glass transition.
We investigate the two-dimensional frustrated quantum Heisenberg model with bond disorder on nearest-neighbor couplings using the recently introduced Foundation Neural-Network Quantum States framework, which enables accurate and efficient computation of disorder-averaged observables with a single variational optimization. Simulations on large lattices reveal an extended region of the phase diagram where conventional magnetic long-range order vanishes in the thermodynamic limit, while the Edwards-Anderson order parameter remains finite, signaling the emergence of a quantum spin-glass phase. These findings, supported by a semiclassical analysis based on a large-spin expansion, provide compelling evidence that the spin glass-order is stable against quantum fluctuations, unlike the classical case where it disappears at any finite temperature.
A quantum ground state of matter is realized in a bosonic model on a three-dimensional fcc lattice with emergent low energy excitations. The phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the graviton, although they have a soft $\ensuremath{\omega}\ensuremath{\sim}{k}^{2}$ dispersion relation. There are three branches of gapless excitations in this phase, one of which is gapless scalar trace mode, the other two have the same polarization and gauge symmetries as the gravitons. The dynamics of this phase is described by a set of Maxwell's equations. The defects carrying gauge charges can drive the system into the superfluid order when the defects are condensed; also the topological defects are coupled to the dual gauge field in the same manner as the charge defects couple to the original gauge field, after the condensation of the topological defects, the system is driven into the Mott insulator phase. In the two-dimensional case, the gapless soft graviton as well as the algebraic liquid phase are destroyed by the vertex operators in the dual theory, and the stripe order is most likely to take place close to the two-dimensional quantum critical point at which the vertex operators are tuned to zero.
Ever since quantum mechanics and relativity appeared at the beginning of the 20th century, physics has been rocked to its foundations. Novel ideas and applications surged relentlessly from the minds of those brave enough to venture into the unknown new worlds revealed by the new sciences. This year marks the centenary of Heisenberg’s quantum mechanics, and the exploration has not waned; rather, the frontiers of our knowledge now extend beyond fundamental theories into the complex playground of symmetry, topology, and emergence. We are faced with the challenge of understanding and predicting the behavior of complex systems in which the interplay of all three is essential for explaining their unique phenomena. Amid such an insurmountable challenge, novel viewpoints and signatures can often guide us through this dense web of complexity. In this doctoral thesis, we explore distinct scenarios where the intertwining of symmetry and topology naturally leads to previously unexplored phenomena, and subtle signatures arise from the combination of old and new theoretical frameworks in the weak and strong coupling regimes. In part one, we study weakly interacting topological phases. In chapter 2, we introduce the idea of time-reversal invariant finite-size topology. We identify signatures of a higher-dimensional bulk topological phase within thin films and wires; we probe this via Wilson loop spectroscopy and electromagnetic responses. Chapter 3 deals with extending previously studied topological skyrmion phases to time-reversal invariant systems. A generalization of the time-reversal parity invariant corresponds to a bulk-boundary texture of the pseudo-spin degrees of freedom. Moreover, our skyrmion invariant is directly linked to a reduced entanglement spectrum with protected spectral flow. Part two of this thesis is dedicated to strongly interacting electrons, where the effective description is that of a network of spins displaying the unconventional physics of spin liquids. In chapter 4, we describe how fractionalization can be generalized in classical spin liquids to yield irrational magnetic moments of dilution clusters. These clusters act as gauge charges for the low-energy lattice gauge theory. Moreover, we show that for a higher-rank gauge theory, distinctive emergent non-decaying spin textures and interactions are hallmarks of the unusual topological magnet. Chapter 5 studies a fragile spin liquid in three dimensions, which displays fractionalization but no algebraically decaying correlations. We find that not only is the Heisenberg model disordered, but the Ising model is as well. Perturbing away, we find a special point where quantum fluctuations stabilize a Z_2 quantum spin liquid.