It is shown that some recently proposed iterative approaches to the ground state of quantum systems can be obtained as zero-temperature limits of free-energy-preserving renormalization transformations, if the perturbative expansion is handled in the appropriate way. Besides giving new insight into the ground-state approaches and their mutual relationships, these results allow us to perform consistent approximate calculations of the free energy at all temperatures and to get global descriptions of the critical properties. Free-energy and specific-heat calculations are reported for $\mathrm{XY}$ and Heisenberg spin-\textonehalf{} chains and for the triangular $\mathrm{XY}$ model. It is also demonstrated how this extension into finite temperatures allows us to compute in a consistent way the $z$ exponent, and to obtain substantial improvement in the numerical values for the ground-state energy density of the transverse Ising model.It is shown that some recently proposed iterative approaches to the ground state of quantum systems can be obtained as zero-temperature limits of free-energy-preserving renormalization transformations, if the perturbative expansion is handled in the appropriate way. Besides giving new insight into the ground-state approaches and their mutual relationships, these results allow us to perform consistent approximate calculations of the free energy at all temperatures and to get global descriptions of the critical properties. Free-energy and specific-heat calculations are reported for $\mathrm{XY}$ and Heisenberg spin-\textonehalf{} chains and for the triangular $\mathrm{XY}$ model. It is also demonstrated how this extension into finite temperatures allows us to compute in a consistent way the $z$ exponent, and to obtain substantial improvement in the numerical values for the ground-state energy density of the transverse Ising model.

Physical review. B, Condensed matterFeb 1, 198333 citations

Quantum spin models at finite temperature

J. Oitmaa, Chris J. Hamer, Weihong Zheng

Cambridge University Press eBooksApr 6, 20060 citations

Ground states of quantum spin systems

Ola Bratteli, Akitaka Kishimoto, Derek W. Robinson

Communications in Mathematical PhysicsDec 1, 197816 citations

Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models

Francisco M. O. Brito, Aires Ferreira

The proliferation of quantum fluctuations and long-range entanglement presents an outstanding challenge for the numerical simulation of interacting spin systems with exotic ground states. Here, we present a toolset of Chebyshev polynomial-based iterative methods that provides a unified framework to study the thermodynamical properties, critical behavior and dynamics of frustrated quantum spin models with controlled accuracy. Similar to previous applications of the Chebyshev spectral methods to condensed matter systems, the algorithmic complexity scales linearly with the Hilbert space dimension and the Chebyshev truncation order. Using this approach, we study two paradigmatic quantum spin models on the honeycomb lattice: the Kitaev-Heisenberg (K-H) and the Kitaev-Ising (K-I) models. We start by applying the Chebyshev toolset to compute nearest-neighbor spin correlations, specific heat and entropy of the K-H model on a 24-spin cluster. Our results are benchmarked against exact diagonalization and a popular iterative method based on thermal pure quantum states. The transitions between a variety of magnetic phases, namely ferromagnetic, Néel, zigzag and stripy antiferromagnetic and quantum spin liquid phases are obtained accurately and efficiently. We also determine the temperature dependence of the spin correlations, over more than three decades in temperature, by means of a finite temperature Chebyshev polynomial method introduced here. Finally, we report novel dynamical signatures of the quantum phase transitions in the K-I model. Our findings suggest that the efficiency, versatility and low-temperature stability of the Chebyshev framework developed here could pave the way for previously unattainable studies of quantum spin models in two dimensions.The proliferation of quantum fluctuations and long-range entanglement presents an outstanding challenge for the numerical simulation of interacting spin systems with exotic ground states. Here, we present a toolset of Chebyshev polynomial-based iterative methods that provides a unified framework to study the thermodynamical properties, critical behavior and dynamics of frustrated quantum spin models with controlled accuracy. Similar to previous applications of the Chebyshev spectral methods to condensed matter systems, the algorithmic complexity scales linearly with the Hilbert space dimension and the Chebyshev truncation order. Using this approach, we study two paradigmatic quantum spin models on the honeycomb lattice: the Kitaev-Heisenberg (K-H) and the Kitaev-Ising (K-I) models. We start by applying the Chebyshev toolset to compute nearest-neighbor spin correlations, specific heat and entropy of the K-H model on a 24-spin cluster. Our results are benchmarked against exact diagonalization and a popular iterative method based on thermal pure quantum states. The transitions between a variety of magnetic phases, namely ferromagnetic, Néel, zigzag and stripy antiferromagnetic and quantum spin liquid phases are obtained accurately and efficiently. We also determine the temperature dependence of the spin correlations, over more than three decades in temperature, by means of a finite temperature Chebyshev polynomial method introduced here. Finally, we report novel dynamical signatures of the quantum phase transitions in the K-I model. Our findings suggest that the efficiency, versatility and low-temperature stability of the Chebyshev framework developed here could pave the way for previously unattainable studies of quantum spin models in two dimensions.

arXiv:2110.01494SciPost Physics CoreFeb 21, 20241 citation

Study of Magnetism in Quantum Spin Systems

Asit Singh

This thesis is divided into 4 chapters. The first chapter gives a brief discussion on the need for the study of Quantum spin systems, and an introduction to Heisenberg Model. In the second chapter, we start the discussion with Quantum entanglement and then go on to show the importance of anti ferromagnetic ground state from the view of entanglement. In the third chapter, we discuss the ways to obtain the ground states of Heisenberg model, both ferromagnet and antiferromagnet. Then we discuss the effect of magnetic field on the antiferromagnetic ground states, for a good understanding of magnetic properties in Chapter(4). In the fourth and the final chapter, we discuss how Bonner Fisher model uses the Bethe ansatz to obtain all the properties of finite Heisenberg chains. Then we analyze the magnetic properties, like Magnetic moment and Susceptibility, of Heisenberg antiferromagnets for finite as well as infinite chains.This thesis is divided into 4 chapters. The first chapter gives a brief discussion on the need for the study of Quantum spin systems, and an introduction to Heisenberg Model. In the second chapter, we start the discussion with Quantum entanglement and then go on to show the importance of anti ferromagnetic ground state from the view of entanglement. In the third chapter, we discuss the ways to obtain the ground states of Heisenberg model, both ferromagnet and antiferromagnet. Then we discuss the effect of magnetic field on the antiferromagnetic ground states, for a good understanding of magnetic properties in Chapter(4). In the fourth and the final chapter, we discuss how Bonner Fisher model uses the Bethe ansatz to obtain all the properties of finite Heisenberg chains. Then we analyze the magnetic properties, like Magnetic moment and Susceptibility, of Heisenberg antiferromagnets for finite as well as infinite chains.

Jan 1, 20110 citations

Two New Methods for Computing Finite Quantum Spin Systems

T. Oguchi, Hidetsugu Kitatani

Springer series in solid-state sciencesJan 1, 19870 citations

\mathrm{XY}

and Heisenberg spin-\textonehalf{} chains and for the triangular

\mathrm{XY}

model. It is also demonstrated how this extension into finite temperatures allows us to compute in a consistent way the

z

exponent, and to obtain substantial improvement in the numerical values for the ground-state energy density of the transverse Ising model.