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:2305.06911 · Physical review. B./Physical review. B

Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders

Bachana Beradze, Mikheil Tsitsishvili, Emanuele Tirrito, Marcello Dalmonte, Titas Chanda, Alexander Nersesyan

Published Aug 21, 2023• 4 citations
arXivHTMLPDF

Abstract

We consider a system of interacting spinless fermions on a two-leg triangular ladder with $\ensuremath{\pi}/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge and a discrete ${\mathbb{Z}}_{2}$ symmetry---a product of parity transformation and chain permutation. Using bosonization, we show that, in the low-energy limit, the system is described by the quantum double-frequency sine-Gordon model. On the basis of this correspondence, a rich phase diagram of the system is obtained. It includes trivial and topological band insulators for weak interactions, separated by a Gaussian critical line, whereas at larger interactions a strongly correlated phase with spontaneously broken ${\mathbb{Z}}_{2}$ symmetry sets in, exhibiting a net charge imbalance and nonzero total current. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry. This non-Abelian symmetry, absent in the microscopic description, is realized at low energies as a combined effect of the magnetic flux, frustration, and many-body correlations. The criticality belongs to the SU(2)${}_{1}$ Wess-Zumino-Novikov-Witten universality class. The critical point bifurcates into two Ising critical lines that separate the band insulators from the strong-coupling symmetry broken phase. We establish an analytical connection between the low-energy description of our model around the critical bifurcation point on one hand and the Ashkin-Teller model and a weakly dimerized $XXZ$ spin-1/2 chain on the other. We complement our field-theory understanding via tensor network simulations, providing compelling quantitative evidences of all bosonization predictions. Our findings are of interest to up-to-date cold atom experiments utilizing Rydberg dressing that have already demonstrated correlated ladder dynamics.

DOI
10.1103/physrevb.108.075146

Related papers

Phase diagram of an interacting staggered Su-Schrieffer-Heeger two-chain ladder close to a quantum critical point

A. A. Nersesyan

We study the ground-state phase diagram of an interacting staggered Su-Schrieffer-Heeger (SSH) ladder in the vicinity of the Gaussian quantum critical point. The corresponding effective field theory, which nonperturbatively treats correlation effects in the ladder, is a double-frequency sine-Gordon (DSG) model. It involves two perturbations at the Gaussian fixed point: the deviation from criticality, and umklapp scattering processes. While massive phases with broken symmetries are identified by means of local order parameters, a topological distinction between thermodynamically equivalent phases becomes feasible only when nonlocal fermionic fields, parity, and the string order parameter are included in consideration. We prove that a noninteracting fermionic staggered SSH ladder is exactly equivalent to an O(2)-symmetric model of two decoupled Kitaev-Majorana chains, or two one-dimensional $p$-wave superconductors. Close to the Gaussian fixed point, the SSH ladder maps to an Ashkin-Teller-like system when interactions are included. Thus, the topological order in the SSH ladder is related to broken-symmetry phases of the associated quantum spin-chain degrees of freedom. The obtained phase diagram includes a Tomonaga-Luttinger liquid state that, due to umklapp processes, can become unstable against either spontaneous dimerization or the onset of a charge-density wave (CDW). In these gapped phases, elementary bulk excitations are quantum kinks carrying the charge ${Q}_{F}=1/2$. For sufficiently strong, long-range interactions, the phase diagram of the model exhibits a bifurcation of the Gaussian critical point into two outgoing Ising criticalities. The latter sandwich a mixed phase in which dimerization coexists with a site-diagonal CDW. In this phase, elementary bulk excitations are represented by two types of topological solitons carrying different fermionic charges, which continuously interpolate between 0 and 1. This phase has also mixed topological properties with coexisting parity and string order parameters.

arXiv:2005.10380•Physical review. B./Physical review. B•Jul 6, 2020•21 citations

Non-Abelian descendant of Abelian duality in a two-dimensional frustrated quantum magnet

Michael Hermele

Several recent works on quantum criticality beyond the Landau-Ginzburg-Wilson paradigm have led to a number of field theories, potentially important for certain two-dimensional magnetic insulating systems, where criticality is not very well understood. This situation highlights the need for nonperturbative information about criticality in two spatial dimensions (three space-time dimensions), which is a longstanding challenge. As a step toward addressing these issues, we present evidence that the O(4) vector model is dual to a theory of Dirac fermions coupled to both SU(2) and U(1) gauge fields. Both field theories arise as low-energy long-wavelength descriptions of a frustrated $XY$ model on the triangular lattice. Abelian boson-vortex duality of the lattice model, together with the emergence of larger non-Abelian symmetry at low energies, leads to this rare example of duality in two spatial dimensions involving non-Abelian global symmetry and fermions but without supersymmetry. The duality can also be viewed as a bosonization of the Dirac fermion gauge theory.

arXiv:0902.1350•Physical Review B•May 28, 2009•7 citations

Critical bifurcation and deconfined quantum criticality in an interacting cluster Ising chain

Sourabh, Bachana Beradze, Mikheil Tsitsishvili +2 more

We investigate the cluster Ising chain with an additional nearest-neighbor interaction using tensor-network methods and a weak-coupling field theory. Without the interaction, the Jordan-Wigner transformation decomposes the model into a triplet of identical Majorana chains related by an exact $O(3)$ flavor symmetry. Their common mass vanishes at the $SU(2)_2$ Wess-Zumino-Novikov-Witten critical point with central charge $c = 3/2$ separating the symmetry-protected topological cluster phase from a ferromagnet. The interaction reduces $O(3)$ to its cyclic subgroup $C_3$, splitting the triplet into a singlet and a doublet whose gaps close separately, producing a critical bifurcation into Ising ($c = 1/2$) and Gaussian ($c = 1$) critical lines. A second ferromagnetic phase opens between these critical lines for repulsive interactions and a disordered phase for attractive ones. The Gaussian line then separates two Landau-incompatible ferromagnets, realizing a deconfined quantum critical line with emergent $O(2)$ symmetry, along which our independently extracted exponents vary continuously yet satisfy the parameter-free relation $β= (2ν- 1)/4$ of the eight-vertex weak universality class. At stronger repulsion this line opens into an extended gapless floating phase with incommensurate algebraic correlations, entered through Berezinskii-Kosterlitz-Thouless transitions. All of these phases and the transitions between them are captured by the weak-coupling theory. Beyond its regime of validity, our simulations reveal a translation-symmetry-breaking antiferromagnet reached through first-order transitions.

cond-mat.str-elCross-listedarXiv:2608.24248•Aug 26, 2026•0 citations

Extended Ashkin-Teller transition in two coupled frustrated Haldane chains

Bowy M. La Rivière, Natalia Chepiga

We report an extremely rich ground-state phase diagram of two spin-1 Haldane chains frustrated with a three-site exchange and coupled by the antiferromagnetic Heisenberg interaction on a zigzag ladder. A particular feature of the phase diagram is the extended quantum phase transition in the Ashkin-Teller universality class that separates the plaquette phase, which spontaneously breaks translation symmetry, and the uniform disordered phase. The former is connected to the Haldane phase, stabilized by large interchain coupling, via the topological Gaussian transition. Upon decreasing the interchain interactions, this intermediate disorder phase vanishes, giving place to a dimerized phase separated from the plaquette phase on one side via a nonmagnetic Ising transition and from the Haldane phase on the other side by a topological weak first-order transition. Finally, in the limit of two decoupled chains, we recover a quantum critical point that corresponds to two copies of the Wess-Zumino-Witten SU ( 2 ) 2 criticality with a total central charge c = 3 .

arXiv:2602.23187•Physical review. B./Physical review. B•Apr 15, 2026•0 citations

Non-Abelian bosonization of the frustrated antiferromagnetic spin-1/2 chain

Dave Allen, David Sénéchal

We study the spin-1/2 chain with nearest-neighbor (${\mathrm{\ensuremath{\kappa}}}_{1}$) and next-nearest-neighbor (${\mathrm{\ensuremath{\kappa}}}_{2}$) interactions in the regime ${\mathrm{\ensuremath{\kappa}}}_{2}$\ensuremath{\gg}:${\mathrm{\ensuremath{\kappa}}}_{1}$, which is equivalent to two chains with a ``zigzag'' interaction. In the continuum limit, this system is described in terms of two coupled level-1 Wess-Zumino-Witten field theories. We illustrate its equivalence with four off-critical Ising models (Majorana fermions). This description is used to investigate the opening of a gap as a function of ${\mathrm{\ensuremath{\kappa}}}_{1}$ and the associated spontaneous breakdown of parity. We calculate the dynamic spin structure factor near the wave vectors accessible to the continuum limit. We comment on the nonzero string order parameter and show the presence of a hidden ${\mathrm{Z}}_{2}$\ifmmode\times\else\texttimes\fi{}${\mathrm{Z}}_{2}$ symmetry via a nonlocal transformation on the microscopic Hamiltonian. For a ferromagnetic interchain coupling, the model is conjectured to be critical, with different velocities for the spin-singlet and spin-triplet excitations.

arXiv:cond-mat/9606007•Physical review. B, Condensed matter•Jan 1, 1997•90 citations

Symmetry-protected topological phases and competing orders in a spin- 1 2 XXZ ladder with a four-spin interaction

Takuhiro Ogino, Shunsuke Furukawa, Ryui Kaneko +2 more

We study a spin-$\frac{1}{2}$ XXZ model with a four-spin interaction on a two-leg ladder. By means of effective field theory and matrix product state calculations, we obtain rich ground-state phase diagrams that consist of eight distinct gapped phases. Four of them exhibit spontaneous symmetry breaking with either a magnetic or valence-bond-solid (VBS) long-range order. The other four are featureless, i.e., the bulk ground state is unique and does not break any symmetry. The featureless phases include the rung singlet (RS) and Haldane phases as well as their variants, the RS* and Haldane* phases, in which twisted singlet pairs $(|\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\rangle}+|\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\rangle})/\sqrt{2}$ are formed between the two legs. We argue and demonstrate that Gaussian transitions with the central charge $c=1$ occur between the featureless phases and between the ordered phases while Ising transitions with $c=1/2$ occur between the featureless and ordered phases. The two types of transition lines cross at the $\mathrm{SU}(2)$-symmetric point, where the criticality is described by the $\mathrm{SU}{(2)}_{2}$ Wess-Zumino-Witten theory with $c=3/2$. The RS-Haldane* and RS*-Haldane transitions give examples of topological phase transitions. Interestingly, the RS* and Haldane* phases, which have highly anisotropic nature, appear even in the vicinity of the isotropic case. We demonstrate that all the four featureless phases are distinguished by topological indices in the presence of certain symmetries.

arXiv:2104.02274•Physical review. B./Physical review. B•Aug 19, 2021•13 citations
We consider a system of interacting spinless fermions on a two-leg triangular ladder with \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/2 magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge and a discrete Z2{\mathbb{Z}}_{2}Z2​ symmetry---a product of parity transformation and chain permutation. Using bosonization, we show that, in the low-energy limit, the system is described by the quantum double-frequency sine-Gordon model. On the basis of this correspondence, a rich phase diagram of the system is obtained. It includes trivial and topological band insulators for weak interactions, separated by a Gaussian critical line, whereas at larger interactions a strongly correlated phase with spontaneously broken Z2{\mathbb{Z}}_{2}Z2​ symmetry sets in, exhibiting a net charge imbalance and nonzero total current. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry. This non-Abelian symmetry, absent in the microscopic description, is realized at low energies as a combined effect of the magnetic flux, frustration, and many-body correlations. The criticality belongs to the SU(2)1{}_{1}1​ Wess-Zumino-Novikov-Witten universality class. The critical point bifurcates into two Ising critical lines that separate the band insulators from the strong-coupling symmetry broken phase. We establish an analytical connection between the low-energy description of our model around the critical bifurcation point on one hand and the Ashkin-Teller model and a weakly dimerized XXZXXZXXZ spin-1/2 chain on the other. We complement our field-theory understanding via tensor network simulations, providing compelling quantitative evidences of all bosonization predictions. Our findings are of interest to up-to-date cold atom experiments utilizing Rydberg dressing that have already demonstrated correlated ladder dynamics.
We study the ground-state phase diagram of an interacting staggered Su-Schrieffer-Heeger (SSH) ladder in the vicinity of the Gaussian quantum critical point. The corresponding effective field theory, which nonperturbatively treats correlation effects in the ladder, is a double-frequency sine-Gordon (DSG) model. It involves two perturbations at the Gaussian fixed point: the deviation from criticality, and umklapp scattering processes. While massive phases with broken symmetries are identified by means of local order parameters, a topological distinction between thermodynamically equivalent phases becomes feasible only when nonlocal fermionic fields, parity, and the string order parameter are included in consideration. We prove that a noninteracting fermionic staggered SSH ladder is exactly equivalent to an O(2)-symmetric model of two decoupled Kitaev-Majorana chains, or two one-dimensional ppp-wave superconductors. Close to the Gaussian fixed point, the SSH ladder maps to an Ashkin-Teller-like system when interactions are included. Thus, the topological order in the SSH ladder is related to broken-symmetry phases of the associated quantum spin-chain degrees of freedom. The obtained phase diagram includes a Tomonaga-Luttinger liquid state that, due to umklapp processes, can become unstable against either spontaneous dimerization or the onset of a charge-density wave (CDW). In these gapped phases, elementary bulk excitations are quantum kinks carrying the charge QF=1/2{Q}_{F}=1/2QF​=1/2. For sufficiently strong, long-range interactions, the phase diagram of the model exhibits a bifurcation of the Gaussian critical point into two outgoing Ising criticalities. The latter sandwich a mixed phase in which dimerization coexists with a site-diagonal CDW. In this phase, elementary bulk excitations are represented by two types of topological solitons carrying different fermionic charges, which continuously interpolate between 0 and 1. This phase has also mixed topological properties with coexisting parity and string order parameters.
Several recent works on quantum criticality beyond the Landau-Ginzburg-Wilson paradigm have led to a number of field theories, potentially important for certain two-dimensional magnetic insulating systems, where criticality is not very well understood. This situation highlights the need for nonperturbative information about criticality in two spatial dimensions (three space-time dimensions), which is a longstanding challenge. As a step toward addressing these issues, we present evidence that the O(4) vector model is dual to a theory of Dirac fermions coupled to both SU(2) and U(1) gauge fields. Both field theories arise as low-energy long-wavelength descriptions of a frustrated XYXYXY model on the triangular lattice. Abelian boson-vortex duality of the lattice model, together with the emergence of larger non-Abelian symmetry at low energies, leads to this rare example of duality in two spatial dimensions involving non-Abelian global symmetry and fermions but without supersymmetry. The duality can also be viewed as a bosonization of the Dirac fermion gauge theory.
We investigate the cluster Ising chain with an additional nearest-neighbor interaction using tensor-network methods and a weak-coupling field theory. Without the interaction, the Jordan-Wigner transformation decomposes the model into a triplet of identical Majorana chains related by an exact O(3)O(3)O(3) flavor symmetry. Their common mass vanishes at the SU(2)2SU(2)_2SU(2)2​ Wess-Zumino-Novikov-Witten critical point with central charge c=3/2c = 3/2c=3/2 separating the symmetry-protected topological cluster phase from a ferromagnet. The interaction reduces O(3)O(3)O(3) to its cyclic subgroup C3C_3C3​, splitting the triplet into a singlet and a doublet whose gaps close separately, producing a critical bifurcation into Ising (c=1/2c = 1/2c=1/2) and Gaussian (c=1c = 1c=1) critical lines. A second ferromagnetic phase opens between these critical lines for repulsive interactions and a disordered phase for attractive ones. The Gaussian line then separates two Landau-incompatible ferromagnets, realizing a deconfined quantum critical line with emergent O(2)O(2)O(2) symmetry, along which our independently extracted exponents vary continuously yet satisfy the parameter-free relation β=(2ν−1)/4β= (2ν- 1)/4β=(2ν−1)/4 of the eight-vertex weak universality class. At stronger repulsion this line opens into an extended gapless floating phase with incommensurate algebraic correlations, entered through Berezinskii-Kosterlitz-Thouless transitions. All of these phases and the transitions between them are captured by the weak-coupling theory. Beyond its regime of validity, our simulations reveal a translation-symmetry-breaking antiferromagnet reached through first-order transitions.
We report an extremely rich ground-state phase diagram of two spin-1 Haldane chains frustrated with a three-site exchange and coupled by the antiferromagnetic Heisenberg interaction on a zigzag ladder. A particular feature of the phase diagram is the extended quantum phase transition in the Ashkin-Teller universality class that separates the plaquette phase, which spontaneously breaks translation symmetry, and the uniform disordered phase. The former is connected to the Haldane phase, stabilized by large interchain coupling, via the topological Gaussian transition. Upon decreasing the interchain interactions, this intermediate disorder phase vanishes, giving place to a dimerized phase separated from the plaquette phase on one side via a nonmagnetic Ising transition and from the Haldane phase on the other side by a topological weak first-order transition. Finally, in the limit of two decoupled chains, we recover a quantum critical point that corresponds to two copies of the Wess-Zumino-Witten SU ( 2 ) 2 criticality with a total central charge c = 3 .
We study the spin-1/2 chain with nearest-neighbor (${\mathrm{\ensuremath{\kappa}}}_{1}$) and next-nearest-neighbor (${\mathrm{\ensuremath{\kappa}}}_{2}$) interactions in the regime ${\mathrm{\ensuremath{\kappa}}}_{2}$\ensuremath{\gg}:${\mathrm{\ensuremath{\kappa}}}_{1}$, which is equivalent to two chains with a ``zigzag'' interaction. In the continuum limit, this system is described in terms of two coupled level-1 Wess-Zumino-Witten field theories. We illustrate its equivalence with four off-critical Ising models (Majorana fermions). This description is used to investigate the opening of a gap as a function of ${\mathrm{\ensuremath{\kappa}}}_{1}$ and the associated spontaneous breakdown of parity. We calculate the dynamic spin structure factor near the wave vectors accessible to the continuum limit. We comment on the nonzero string order parameter and show the presence of a hidden Z2{\mathrm{Z}}_{2}Z2​\ifmmode\times\else\texttimes\fi{}Z2{\mathrm{Z}}_{2}Z2​ symmetry via a nonlocal transformation on the microscopic Hamiltonian. For a ferromagnetic interchain coupling, the model is conjectured to be critical, with different velocities for the spin-singlet and spin-triplet excitations.
We study a spin-12\frac{1}{2}21​ XXZ model with a four-spin interaction on a two-leg ladder. By means of effective field theory and matrix product state calculations, we obtain rich ground-state phase diagrams that consist of eight distinct gapped phases. Four of them exhibit spontaneous symmetry breaking with either a magnetic or valence-bond-solid (VBS) long-range order. The other four are featureless, i.e., the bulk ground state is unique and does not break any symmetry. The featureless phases include the rung singlet (RS) and Haldane phases as well as their variants, the RS* and Haldane* phases, in which twisted singlet pairs $(|\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\rangle}+|\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\rangle})/\sqrt{2}$ are formed between the two legs. We argue and demonstrate that Gaussian transitions with the central charge c=1c=1c=1 occur between the featureless phases and between the ordered phases while Ising transitions with c=1/2c=1/2c=1/2 occur between the featureless and ordered phases. The two types of transition lines cross at the SU(2)\mathrm{SU}(2)SU(2)-symmetric point, where the criticality is described by the SU(2)2\mathrm{SU}{(2)}_{2}SU(2)2​ Wess-Zumino-Witten theory with c=3/2c=3/2c=3/2. The RS-Haldane* and RS*-Haldane transitions give examples of topological phase transitions. Interestingly, the RS* and Haldane* phases, which have highly anisotropic nature, appear even in the vicinity of the isotropic case. We demonstrate that all the four featureless phases are distinguished by topological indices in the presence of certain symmetries.