We investigate quantum order by disorder in a frustrated spin nanotube formed by wrapping a $J_1$ - $J_2$ Heisenberg model at 45 $^\circ$ around a cylinder. Using Schwinger boson theory and Density Matrix Renormalization Group (DMRG), we have computed the ground-state phase diagram to reveal a $\mathbb{Z}_2$ phase in which collinear spin stripes form a right or left handed helix around the nanotube. We have derived an analytic estimate for the critical $η_c=J_1/2J_2$ of the $\mathbb{Z}_2$ helical phase transition, which is in agreement with the DMRG results. By evaluating the entanglement spectrum and nonlocal string order parameters we discuss the topology of the $\mathbb{Z}_2$ -helical phase.We investigate quantum order by disorder in a frustrated spin nanotube formed by wrapping a $J_1$-$J_2$ Heisenberg model at 45$^\circ$ around a cylinder. Using Schwinger boson theory and Density Matrix Renormalization Group (DMRG), we have computed the ground-state phase diagram to reveal a $\mathbb{Z}_2$ phase in which collinear spin stripes form a right or left handed helix around the nanotube. We have derived an analytic estimate for the critical $η_c=J_1/2J_2$ of the $\mathbb{Z}_2$ helical phase transition, which is in agreement with the DMRG results. By evaluating the entanglement spectrum and nonlocal string order parameters we discuss the topology of the $\mathbb{Z}_2$-helical phase.

arXiv:2303.04690Mar 8, 20230 citations

Curvature induced quantum potential on deformed surfaces

Victor Atanasov, Rossen Dandoloff

arXiv:0803.3391Physics Letters AAug 24, 200730 citations

A quantum mechanical curvature theorem

Jeremiah N. Silverman, Jon C. van Leuven

Chemical Physics LettersOct 1, 197023 citations

Quantum geometric potential induced conformational transitions in elastic helical nanoribbons

Radha Balakrishnan, Rossen Dandoloff, Avadh Saxena

We consider an {\em elastic} helical nanoribbon that can take on various conformations, and study the effect of placing a quantum particle on its curved surface. Using a modified Canham-Helfrich model for the elastic energy, we write down the local elastic potential for the ribbon in terms of its bending rigidity, mean curvature $M$ and Gaussian curvature $K$ . The Schrödinger equation of a particle confined to a {\em rigid} curved surface is found using da Costa's formulation. It has a purely quantum geometric potential which depends on $M$ and $K$ . The Schrödinger equation of a particle on an {\em elastic } curved surface will therefore have a total potential comprising quantum and elastic potentials. We compute $M$ and $K$ for a helical ribbon and derive the total potential which depends on the conformation and is thus geometric in nature. Defining a dimensionless quantity $R_H$ , we study the behavior of the total geometric potential as $R_H$ is varied. In the absence of an electron, the elastic potential is positive and has a single positive maximum for all conformations. Further, a binormal helical ribbon conformation has the lowest potential, while the normal ribbon has the highest, with those of the intermediate ribbons lying in between these. Intriguingly, when a quantum particle is placed on the elastic ribbon, above a certain critical value of $R_H$ , the presence of the quantum geometric potential {\em reverses} this order. But localized states for the particle are not supported. Only above a second critical value of $R_H$ , localized states appear for all conformations. The injection of an electron on {\it any} given conformation of the elastic ribbon will induce a conformational transition to the normal ribbon conformation.We consider an {\em elastic} helical nanoribbon that can take on various conformations, and study the effect of placing a quantum particle on its curved surface. Using a modified Canham-Helfrich model for the elastic energy, we write down the local elastic potential for the ribbon in terms of its bending rigidity, mean curvature $M$ and Gaussian curvature $K$. The Schrödinger equation of a particle confined to a {\em rigid} curved surface is found using da Costa's formulation. It has a purely quantum geometric potential which depends on $M$ and $K$. The Schrödinger equation of a particle on an {\em elastic } curved surface will therefore have a total potential comprising quantum and elastic potentials. We compute $M$ and $K$ for a helical ribbon and derive the total potential which depends on the conformation and is thus geometric in nature. Defining a dimensionless quantity $R_H$, we study the behavior of the total geometric potential as $R_H$ is varied. In the absence of an electron, the elastic potential is positive and has a single positive maximum for all conformations. Further, a binormal helical ribbon conformation has the lowest potential, while the normal ribbon has the highest, with those of the intermediate ribbons lying in between these. Intriguingly, when a quantum particle is placed on the elastic ribbon, above a certain critical value of $R_H$, the presence of the quantum geometric potential {\em reverses} this order. But localized states for the particle are not supported. Only above a second critical value of $R_H$, localized states appear for all conformations. The injection of an electron on {\it any} given conformation of the elastic ribbon will induce a conformational transition to the normal ribbon conformation.

quant-pharXiv:2607.29623Aug 3, 20260 citations

Quantum order by disorder in frustrated spin nanotubes

João C. Getelina, Zekun Zhuang, Premala Chandra +3 more

We investigate quantum order by disorder in a frustrated spin nanotube formed by wrapping a ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model at ${45}^{\ensuremath{\circ}}$ around a cylinder. Using Schwinger boson theory and density matrix renormalization group (DMRG), we have computed the ground-state phase diagram to reveal a ${\mathbb{Z}}_{2}$ phase in which collinear spin stripes form a right- or left-handed helix around the nanotube. We have derived an analytic estimate for the critical ${\ensuremath{\eta}}_{c}={J}_{1}/2{J}_{2}$ of the ${\mathbb{Z}}_{2}$ -helical phase transition, which is in agreement with the DMRG results. By evaluating the entanglement spectrum and nonlocal string order parameters we discuss the topology of the ${\mathbb{Z}}_{2}$ -helical phase.We investigate quantum order by disorder in a frustrated spin nanotube formed by wrapping a ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model at ${45}^{\ensuremath{\circ}}$ around a cylinder. Using Schwinger boson theory and density matrix renormalization group (DMRG), we have computed the ground-state phase diagram to reveal a ${\mathbb{Z}}_{2}$ phase in which collinear spin stripes form a right- or left-handed helix around the nanotube. We have derived an analytic estimate for the critical ${\ensuremath{\eta}}_{c}={J}_{1}/2{J}_{2}$ of the ${\mathbb{Z}}_{2}$-helical phase transition, which is in agreement with the DMRG results. By evaluating the entanglement spectrum and nonlocal string order parameters we discuss the topology of the ${\mathbb{Z}}_{2}$-helical phase.

Physical review. B./Physical review. BFeb 16, 20243 citations

We investigate quantum order by disorder in a frustrated spin nanotube formed by wrapping a

J_1

J_2

Heisenberg model at 45

^\circ

around a cylinder. Using Schwinger boson theory and Density Matrix Renormalization Group (DMRG), we have computed the ground-state phase diagram to reveal a

\mathbb{Z}_2

phase in which collinear spin stripes form a right or left handed helix around the nanotube. We have derived an analytic estimate for the critical

η_c=J_1/2J_2

of the

\mathbb{Z}_2

helical phase transition, which is in agreement with the DMRG results. By evaluating the entanglement spectrum and nonlocal string order parameters we discuss the topology of the

\mathbb{Z}_2

-helical phase.

M

and Gaussian curvature

K

. The Schrödinger equation of a particle confined to a {\em rigid} curved surface is found using da Costa's formulation. It has a purely quantum geometric potential which depends on

M

and

K

. The Schrödinger equation of a particle on an {\em elastic } curved surface will therefore have a total potential comprising quantum and elastic potentials. We compute

M

and

K

for a helical ribbon and derive the total potential which depends on the conformation and is thus geometric in nature. Defining a dimensionless quantity

R_H

, we study the behavior of the total geometric potential as

R_H

is varied. In the absence of an electron, the elastic potential is positive and has a single positive maximum for all conformations. Further, a binormal helical ribbon conformation has the lowest potential, while the normal ribbon has the highest, with those of the intermediate ribbons lying in between these. Intriguingly, when a quantum particle is placed on the elastic ribbon, above a certain critical value of

R_H

, the presence of the quantum geometric potential {\em reverses} this order. But localized states for the particle are not supported. Only above a second critical value of

R_H

, localized states appear for all conformations. The injection of an electron on {\it any} given conformation of the elastic ribbon will induce a conformational transition to the normal ribbon conformation.

{\mathbb{Z}}_{2}

phase in which collinear spin stripes form a right- or left-handed helix around the nanotube. We have derived an analytic estimate for the critical ${\ensuremath{\eta}}_{c}={J}_{1}/2{J}_{2}$ of the

{\mathbb{Z}}_{2}

-helical phase transition, which is in agreement with the DMRG results. By evaluating the entanglement spectrum and nonlocal string order parameters we discuss the topology of the

{\mathbb{Z}}_{2}

-helical phase.