We propose a new method of constructing the quantum Griffiths inequality. From a viewpoint of operator inequalities, we first study the quantum rotor model. This viewpoint clarifies important connections between the reflection positivity and the Griffiths inequality. Next we apply our method to the spin- $1/2$ quantum Heisenberg model. Finally we point out a model-independent structure which governs the correlation inequalities.We propose a new method of constructing the quantum Griffiths inequality. From a viewpoint of operator inequalities, we first study the quantum rotor model. This viewpoint clarifies important connections between the reflection positivity and the Griffiths inequality. Next we apply our method to the spin-$1/2$ quantum Heisenberg model. Finally we point out a model-independent structure which governs the correlation inequalities.

arXiv:1504.06676Apr 25, 20150 citations

Positivity for Matrix Systems: A Case Study from Quantum Mechanics

Claudio Altafini

Lecture notes in control and information sciencesApr 30, 20041 citation

COMPLETE POSITIVITY AND OPEN QUANTUM SYSTEMS

Rebolledo Berroeta, Rolando Aquiles

Jan 1, 20010 citations

Graviton-mediated entanglement due to light bending from a quantum rotor

Dripto Biswas, Sougato Bose, Anupam Mazumdar +1 more

One of the key tests of the quantum nature of gravity is to test whether the virtual mediator of gravity between matter and photon gives rise to the quantum light-bending phenomenon. The off-shell degrees of freedom, involving the spin-2 and spin-0 components of graviton, reproduce the classical deviation of light rays, as well as have been predicted to generate entanglement between matter and photon. This paper explores the generation of entanglement due to the quantum gravitational interaction in an optomechanical setup with a quantum rotor and photon. The virtual exchange of a graviton provides entanglement between the photon degrees of freedom and the spatial position of the quantum rotor, with the rotational state affecting its magnitude. We analyze the case of a high spinning rotor, in an approximately classical state of angular momentum, and quantify its effect on the gravitationally induced entanglement between the photon and the position of the quantum rotor. We show that the difference in the linear entanglement entropies, of prograde-and-retrograde motion of the photon with respect to the quantum rotor, provide tangible observable consequences.One of the key tests of the quantum nature of gravity is to test whether the virtual mediator of gravity between matter and photon gives rise to the quantum light-bending phenomenon. The off-shell degrees of freedom, involving the spin-2 and spin-0 components of graviton, reproduce the classical deviation of light rays, as well as have been predicted to generate entanglement between matter and photon. This paper explores the generation of entanglement due to the quantum gravitational interaction in an optomechanical setup with a quantum rotor and photon. The virtual exchange of a graviton provides entanglement between the photon degrees of freedom and the spatial position of the quantum rotor, with the rotational state affecting its magnitude. We analyze the case of a high spinning rotor, in an approximately classical state of angular momentum, and quantify its effect on the gravitationally induced entanglement between the photon and the position of the quantum rotor. We show that the difference in the linear entanglement entropies, of prograde-and-retrograde motion of the photon with respect to the quantum rotor, provide tangible observable consequences.

quant-pharXiv:2606.09991Jun 10, 2026

Quantum rotors on the AB2 chain with competing interactions

Antônio Sandoildo Freitas Tenório, R. R. Montenegro-Filho, Mauricio D. Coutinho-Filho

We present the ground-state phase diagram of $q=1/2$ quantum-rotor chains with competing interactions (frustration) calculated through cluster variational mean field approaches. We consider two interaction patterns, named ${\text{F}}_{1}$ and ${\text{F}}_{2}$ models, between the quantum-rotor momentum and position operators, which follow exchange patterns of known one-dimensional spin-1/2 systems with a ferrimagnetic state in their phase diagrams. The spin-1/2 ${\text{F}}_{1}$ model is known as the diamond chain and is related to the azurite compound, while the spin-1/2 ${\text{F}}_{2}$ model was recently shown to present a frustration-induced condensation of magnons. We provide a detailed comparison between the quantum-rotor phase diagrams, in single- and multisite mean-field approaches, and known results for the spin-1/2 models, including exact diagonalization and density matrix renormalization group data for these systems, as well as phase diagrams of the associated classical models.We present the ground-state phase diagram of $q=1/2$ quantum-rotor chains with competing interactions (frustration) calculated through cluster variational mean field approaches. We consider two interaction patterns, named ${\text{F}}_{1}$ and ${\text{F}}_{2}$ models, between the quantum-rotor momentum and position operators, which follow exchange patterns of known one-dimensional spin-1/2 systems with a ferrimagnetic state in their phase diagrams. The spin-1/2 ${\text{F}}_{1}$ model is known as the diamond chain and is related to the azurite compound, while the spin-1/2 ${\text{F}}_{2}$ model was recently shown to present a frustration-induced condensation of magnons. We provide a detailed comparison between the quantum-rotor phase diagrams, in single- and multisite mean-field approaches, and known results for the spin-1/2 models, including exact diagonalization and density matrix renormalization group data for these systems, as well as phase diagrams of the associated classical models.

arXiv:1602.05383Physical Review BAug 17, 20099 citations

1/2

quantum Heisenberg model. Finally we point out a model-independent structure which governs the correlation inequalities.

We present the ground-state phase diagram of

q=1/2

quantum-rotor chains with competing interactions (frustration) calculated through cluster variational mean field approaches. We consider two interaction patterns, named

{\text{F}}_{1}

and

{\text{F}}_{2}

models, between the quantum-rotor momentum and position operators, which follow exchange patterns of known one-dimensional spin-1/2 systems with a ferrimagnetic state in their phase diagrams. The spin-1/2

{\text{F}}_{1}

model is known as the diamond chain and is related to the azurite compound, while the spin-1/2

{\text{F}}_{2}

model was recently shown to present a frustration-induced condensation of magnons. We provide a detailed comparison between the quantum-rotor phase diagrams, in single- and multisite mean-field approaches, and known results for the spin-1/2 models, including exact diagonalization and density matrix renormalization group data for these systems, as well as phase diagrams of the associated classical models.