A strongly-coupled zig-zag transition

The spin-1/2 antiferromagnetic zig-zag ladder is studied by exact diagonalization of small systems in the regime of weak interchain coupling. A gapless phase with quasi-long-range spiral correlations has been predicted to occur in this regime if easy-plane $(\mathrm{XY})$ anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase, and a spiral phase. We study the level crossings of the spectrum, the dimer correlation function, the structure factor, and the spin stiffness within these phases, as well as at the transition points. As the interchain coupling decreases we observe a transition in the anisotropic $\mathrm{XY}$ case from a phase with a gap to a gapless phase that is best described by two decoupled antiferromagnetic chains. The isotropic and the anisotropic $\mathrm{XY}$ cases are found to be qualitatively the same, however, in the regime of weak interchain coupling for the small systems studied here. We attribute this to a finite-size effect in the isotropic zig-zag case that results from exponentially diverging antiferromagnetic correlations in the weak-coupling limit.The spin-1/2 antiferromagnetic zig-zag ladder is studied by exact diagonalization of small systems in the regime of weak interchain coupling. A gapless phase with quasi-long-range spiral correlations has been predicted to occur in this regime if easy-plane $(\mathrm{XY})$ anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase, and a spiral phase. We study the level crossings of the spectrum, the dimer correlation function, the structure factor, and the spin stiffness within these phases, as well as at the transition points. As the interchain coupling decreases we observe a transition in the anisotropic $\mathrm{XY}$ case from a phase with a gap to a gapless phase that is best described by two decoupled antiferromagnetic chains. The isotropic and the anisotropic $\mathrm{XY}$ cases are found to be qualitatively the same, however, in the regime of weak interchain coupling for the small systems studied here. We attribute this to a finite-size effect in the isotropic zig-zag case that results from exponentially diverging antiferromagnetic correlations in the weak-coupling limit.

arXiv:cond-mat/0104090Physical review. B, Condensed matterMay 22, 20017 citations

A strongly coupled zig-zag transition

Vijay Balasubramanian, Micha Berkooz, Simon F. Ross +1 more

Abstract The zig-zag symmetry transition is a phase transition in 1D quantum wires, in which a Wigner lattice of electrons transitions to two staggered lattices. Previous studies model this transition as a Luttinger liquid coupled to a Majorana fermion. The model exhibits interesting RG flows, involving quenching of velocities in subsectors of the theory. We suggest an extension of the model which replaces the Majorana fermion by a more general CFT; this includes an experimentally realizable case with two Majorana fermions. We analyse the RG flow both in field theory and using AdS/CFT techniques in the large central charge limit of the CFT. The model has a rich phase structure with new qualitative features, already in the two Majorana fermion case. The AdS/CFT calculation involves considering back reaction in space-time to capture subleading effects.Abstract The zig-zag symmetry transition is a phase transition in 1D quantum wires, in which a Wigner lattice of electrons transitions to two staggered lattices. Previous studies model this transition as a Luttinger liquid coupled to a Majorana fermion. The model exhibits interesting RG flows, involving quenching of velocities in subsectors of the theory. We suggest an extension of the model which replaces the Majorana fermion by a more general CFT; this includes an experimentally realizable case with two Majorana fermions. We analyse the RG flow both in field theory and using AdS/CFT techniques in the large central charge limit of the CFT. The model has a rich phase structure with new qualitative features, already in the two Majorana fermion case. The AdS/CFT calculation involves considering back reaction in space-time to capture subleading effects.

arXiv:1305.3574Journal of High Energy PhysicsSep 1, 20130 citations

A shaking phase transition

Bryce Gadway

Nature PhysicsMar 1, 20221 citation

A strongly coupled zig-zag transition

Vijay Balasubramanian, Micha Berkooz A, Simon F. Ross

The zig-zag symmetry transition is a phase transition in 1D quantum wires, in which a Wigner lattice of electrons transitions to two staggered lattices. Pre-vious studies model this transition as a Luttinger liquid coupled to a Majorana fermion. The model exhibits interesting RG flows, involving quenching of ve-locities in subsectors of the theory. We suggest an extension of the model which replaces the Majorana fermion by a more general CFT; this includes an exper-imentally realizable case with two Majorana fermions. We analyse the RG flow both in field theory and using AdS/CFT techniques in the large central charge limit of the CFT. The model has a rich phase structure with new qualitative features, already in the two Majorana fermion case. The AdS/CFT calculation involves considering back reaction in space-time to capture subleading effects.The zig-zag symmetry transition is a phase transition in 1D quantum wires, in which a Wigner lattice of electrons transitions to two staggered lattices. Pre-vious studies model this transition as a Luttinger liquid coupled to a Majorana fermion. The model exhibits interesting RG flows, involving quenching of ve-locities in subsectors of the theory. We suggest an extension of the model which replaces the Majorana fermion by a more general CFT; this includes an exper-imentally realizable case with two Majorana fermions. We analyse the RG flow both in field theory and using AdS/CFT techniques in the large central charge limit of the CFT. The model has a rich phase structure with new qualitative features, already in the two Majorana fermion case. The AdS/CFT calculation involves considering back reaction in space-time to capture subleading effects.

Aug 14, 20160 citations

Transition to a Relaxation-Free Regime

Marine Pigneur

Springer thesesJan 1, 20200 citations

(\mathrm{XY})

anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase, and a spiral phase. We study the level crossings of the spectrum, the dimer correlation function, the structure factor, and the spin stiffness within these phases, as well as at the transition points. As the interchain coupling decreases we observe a transition in the anisotropic

\mathrm{XY}

case from a phase with a gap to a gapless phase that is best described by two decoupled antiferromagnetic chains. The isotropic and the anisotropic

\mathrm{XY}

cases are found to be qualitatively the same, however, in the regime of weak interchain coupling for the small systems studied here. We attribute this to a finite-size effect in the isotropic zig-zag case that results from exponentially diverging antiferromagnetic correlations in the weak-coupling limit.