We uncover a novel mechanism for inducing a gapful phase in interacting many-body quantum chains. The mechanism is nonperturbative, being triggered only in the presence of both strong interactions and strong aperiodic (disordered) modulation. In the context of the critical antiferromagnetic spin-1/2 XXZ chain, we identify an emerging dimerization which removes the system from criticality and stabilizes the novel phase. This mechanism is shown to be quite general in strongly interacting quantum chains in the presence of strongly modulated quasiperiodic disorder which is, surprisingly, perturbatively irrelevant. Finally, we also characterize the associated quantum phase transition via the corresponding critical exponents and thermodynamic properties.We uncover a novel mechanism for inducing a gapful phase in interacting many-body quantum chains. The mechanism is nonperturbative, being triggered only in the presence of both strong interactions and strong aperiodic (disordered) modulation. In the context of the critical antiferromagnetic spin-1/2 XXZ chain, we identify an emerging dimerization which removes the system from criticality and stabilizes the novel phase. This mechanism is shown to be quite general in strongly interacting quantum chains in the presence of strongly modulated quasiperiodic disorder which is, surprisingly, perturbatively irrelevant. Finally, we also characterize the associated quantum phase transition via the corresponding critical exponents and thermodynamic properties.

Oct 3, 20190 citations

Localization and emergent dimerization in aperiodic quantum spin chains

André P. Vieira, José A. Hoyos

We report on a novel mechanism for the generation of a mass gap in critical antiferromagnetic quantum XXZ spin-\frac{1}{2} chains. This mechanism is induced by perturbing the chains with aperiodic (but deterministic) nearest-neighbor coupling constants. In the limit of weak perturbations, such aperiodicity is shown to be irrelevant in the renormalization-group sense for any anisotropy parameter. Upon increasing the aperiodicity beyond the perturbation limit, an energy gap appears above the ground state, provided that anisotropy is not too strong (i.e. the system is sufficiently far from the noninteracting XX limit). Using a strong-disorder renormalization-group technique, we are able to relate the energy gap to an emergent dimerization of the low-energy effective coupling constants. Our results are further confirmed by quantum Monte Carlo and density-matrix renormalization-group calculations, from which we also estimate the critical exponents of the corresponding transition.We report on a novel mechanism for the generation of a mass gap in critical antiferromagnetic quantum XXZ spin-\frac{1}{2} chains. This mechanism is induced by perturbing the chains with aperiodic (but deterministic) nearest-neighbor coupling constants. In the limit of weak perturbations, such aperiodicity is shown to be irrelevant in the renormalization-group sense for any anisotropy parameter. Upon increasing the aperiodicity beyond the perturbation limit, an energy gap appears above the ground state, provided that anisotropy is not too strong (i.e. the system is sufficiently far from the noninteracting XX limit). Using a strong-disorder renormalization-group technique, we are able to relate the energy gap to an emergent dimerization of the low-energy effective coupling constants. Our results are further confirmed by quantum Monte Carlo and density-matrix renormalization-group calculations, from which we also estimate the critical exponents of the corresponding transition.

Apr 13, 20181 citation

Quasiperiodic Quantum Ising Transitions in 1D

Philip J. D. Crowley, Anushya Chandran, Chris R. Laumann

Unlike random potentials, quasiperiodic modulation can induce localization-delocalization transitions in one dimension. In this Letter, we analyze the implications of this for symmetry breaking in the quasiperiodically modulated quantum Ising chain. Although weak modulation is irrelevant, strong modulation induces new ferromagnetic and paramagnetic phases which are fully localized and gapless. The quasiperiodic potential and localized excitations lead to quantum criticality that is intermediate to that of the clean and randomly disordered models with exponents of ν=1^{+} (exact) and z≈1.9, Δ_{σ}≈0.16, and Δ_{γ}≈0.63 (up to logarithmic corrections). Technically, the clean Ising transition is destabilized by logarithmic wandering of the local reduced couplings. We conjecture that the wandering coefficient w controls the universality class of the quasiperiodic transition and show its stability to smooth perturbations that preserve the quasiperiodic structure of the model.Unlike random potentials, quasiperiodic modulation can induce localization-delocalization transitions in one dimension. In this Letter, we analyze the implications of this for symmetry breaking in the quasiperiodically modulated quantum Ising chain. Although weak modulation is irrelevant, strong modulation induces new ferromagnetic and paramagnetic phases which are fully localized and gapless. The quasiperiodic potential and localized excitations lead to quantum criticality that is intermediate to that of the clean and randomly disordered models with exponents of ν=1^{+} (exact) and z≈1.9, Δ_{σ}≈0.16, and Δ_{γ}≈0.63 (up to logarithmic corrections). Technically, the clean Ising transition is destabilized by logarithmic wandering of the local reduced couplings. We conjecture that the wandering coefficient w controls the universality class of the quasiperiodic transition and show its stability to smooth perturbations that preserve the quasiperiodic structure of the model.

arXiv:1801.07269Physical Review LettersApr 24, 201832 citations

Universality and quantum criticality in quasiperiodic spin chains

Utkarsh Agrawal, Sarang Gopalakrishnan, Romain Vasseur

Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems and disordered ones as well. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization-group transformation. These discrete sequences are therefore fixed points of a functional renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition.Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems and disordered ones as well. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization-group transformation. These discrete sequences are therefore fixed points of a functional renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition.

arXiv:1908.02774Nature CommunicationsMay 6, 202053 citations

Floating, critical, and dimerized phases in a frustrated spin- 32 chain

Natalia Chepiga, Ian K. Affleck, Frédéric Mila

We study spontaneous dimerization and emergent criticality in a spin- $\frac{3}{2}$ chain with antiferromagnetic nearest-neighbor ${J}_{1}$ , next-nearest-neighbor ${J}_{2}$ , and three-site ${J}_{3}$ interactions. In the absence of three-site interaction ${J}_{3}$ , we provide evidence that the model undergoes a remarkable sequence of three phase transitions as a function of ${J}_{2}/{J}_{1}$ , going successively through a critical-commensurate phase, a partially dimerized gapped phase, a critical floating phase with quasi-long-range incommensurate order, to end up in a fully dimerized phase at very large ${J}_{2}/{J}_{1}$ . In the field-theory language, this implies that the coupling constant of the marginal operator responsible for dimerization changes sign three times. For large enough ${J}_{3}$ , the fully dimerized phase is stabilized for all ${J}_{2}$ , and the phase transitions between the critical phases and this phase are both Wess-Zumino-Witten (WZW) SU(2) ${}_{3}$ along part of the boundary and turn first order at some point due to the presence of a marginal operator in the WZW SU(2) ${}_{3}$ model. By contrast, the transition between the two-dimerized phase is always first order, and the phase transitions between the partially dimerized phase and the critical phases are Kosterlitz-Thouless. Finally, we discuss the intriguing spin- $\frac{1}{2}$ edge states that emerge in the partially dimerized phase for even chains. Unlike their counterparts in the spin-1 chain, they are not confined and disappear upon increasing ${J}_{2}$ in favor of a reorganization of the dimerization pattern.We study spontaneous dimerization and emergent criticality in a spin-$\frac{3}{2}$ chain with antiferromagnetic nearest-neighbor ${J}_{1}$, next-nearest-neighbor ${J}_{2}$, and three-site ${J}_{3}$ interactions. In the absence of three-site interaction ${J}_{3}$, we provide evidence that the model undergoes a remarkable sequence of three phase transitions as a function of ${J}_{2}/{J}_{1}$, going successively through a critical-commensurate phase, a partially dimerized gapped phase, a critical floating phase with quasi-long-range incommensurate order, to end up in a fully dimerized phase at very large ${J}_{2}/{J}_{1}$. In the field-theory language, this implies that the coupling constant of the marginal operator responsible for dimerization changes sign three times. For large enough ${J}_{3}$, the fully dimerized phase is stabilized for all ${J}_{2}$, and the phase transitions between the critical phases and this phase are both Wess-Zumino-Witten (WZW) SU(2)${}_{3}$ along part of the boundary and turn first order at some point due to the presence of a marginal operator in the WZW SU(2)${}_{3}$ model. By contrast, the transition between the two-dimerized phase is always first order, and the phase transitions between the partially dimerized phase and the critical phases are Kosterlitz-Thouless. Finally, we discuss the intriguing spin-$\frac{1}{2}$ edge states that emerge in the partially dimerized phase for even chains. Unlike their counterparts in the spin-1 chain, they are not confined and disappear upon increasing ${J}_{2}$ in favor of a reorganization of the dimerization pattern.

arXiv:2002.08982Physical review. B./Physical review. BMay 5, 202017 citations

Topological quantum criticality in the quasiperiodic cluster Ising chain

Sheng Yang, Hai-Qing Lin, Xue-Jia Yu

Topological classifications of quantum critical systems have recently attracted growing interest, as they go beyond the traditional paradigms of condensed matter and statistical physics. However, such classifications remain largely unexplored in aperiodic environments, particularly under quasiperiodic modulations. In this Letter, we uncover a family of topological quasiperiodic fixed points with critical scalings intermediate between the clean and infinite-randomness limits. By exactly solving the quasiperiodic cluster-Ising chain, we demonstrate that all phase boundaries separating quasiperiodically modulated phases are governed by topological Ising-like fixed points unique to strongly modulated quasiperiodic systems. Although their local bulk critical properties match those of conventional quasiperiodic Ising critical points reported before, these fixed points host robust topological edge degeneracies and exhibit a distinct symmetry-enriched realization of the quasiperiodic Ising criticality, as further supported by complementary lattice simulations.Topological classifications of quantum critical systems have recently attracted growing interest, as they go beyond the traditional paradigms of condensed matter and statistical physics. However, such classifications remain largely unexplored in aperiodic environments, particularly under quasiperiodic modulations. In this Letter, we uncover a family of topological quasiperiodic fixed points with critical scalings intermediate between the clean and infinite-randomness limits. By exactly solving the quasiperiodic cluster-Ising chain, we demonstrate that all phase boundaries separating quasiperiodically modulated phases are governed by topological Ising-like fixed points unique to strongly modulated quasiperiodic systems. Although their local bulk critical properties match those of conventional quasiperiodic Ising critical points reported before, these fixed points host robust topological edge degeneracies and exhibit a distinct symmetry-enriched realization of the quasiperiodic Ising criticality, as further supported by complementary lattice simulations.

arXiv:2602.01223Physical Review LettersOct 26, 20260 citations

We study spontaneous dimerization and emergent criticality in a spin-

\frac{3}{2}

chain with antiferromagnetic nearest-neighbor

{J}_{1}

, next-nearest-neighbor

{J}_{2}

, and three-site

{J}_{3}

interactions. In the absence of three-site interaction

{J}_{3}

, we provide evidence that the model undergoes a remarkable sequence of three phase transitions as a function of

{J}_{2}/{J}_{1}

, going successively through a critical-commensurate phase, a partially dimerized gapped phase, a critical floating phase with quasi-long-range incommensurate order, to end up in a fully dimerized phase at very large

{J}_{2}/{J}_{1}

. In the field-theory language, this implies that the coupling constant of the marginal operator responsible for dimerization changes sign three times. For large enough

{J}_{3}

, the fully dimerized phase is stabilized for all

{J}_{2}

, and the phase transitions between the critical phases and this phase are both Wess-Zumino-Witten (WZW) SU(2)

{}_{3}

along part of the boundary and turn first order at some point due to the presence of a marginal operator in the WZW SU(2)

{}_{3}

model. By contrast, the transition between the two-dimerized phase is always first order, and the phase transitions between the partially dimerized phase and the critical phases are Kosterlitz-Thouless. Finally, we discuss the intriguing spin-

\frac{1}{2}

edge states that emerge in the partially dimerized phase for even chains. Unlike their counterparts in the spin-1 chain, they are not confined and disappear upon increasing

{J}_{2}

in favor of a reorganization of the dimerization pattern.