scholarly journals Thermodynamics of General Heisenberg Spin Tetramers Composed of Coupled Quantum Dimers

2021 ◽  
Vol 7 (2) ◽  
pp. 29
Author(s):  
Peter Dyszel ◽  
Jason T. Haraldsen
Keyword(s):  
Quantum Computing ◽  
Data Storage ◽  
Spin Exchange ◽  
Energy Levels ◽  
Exchange Interactions ◽  
Analytic Solutions ◽  
Quantum Spin ◽  
Molecular Magnets ◽  
Heisenberg Spin ◽  
Schottky Anomaly

Advances in quantum computing technology have been made in recent years due to the evolution of spin clusters. Recent studies have tended towards spin cluster subgeometries to understand more complex structures better. These molecular magnets provide a multitude of phenomena via exchange interactions that allow for advancements in spintronics and other magnetic system applications due to the possibility of increasing speed, data storage, memory, and stability of quantum computing systems. Using the Heisenberg spin–spin exchange Hamiltonian and exact diagonalization, we examine the evolution of quantum energy levels and thermodynamic properties for various spin configurations and exchange interactions. The XXYY quantum spin tetramer considered in this study consists of two coupled dimers with exchange interactions α1J and α1′J and a dimer–dimer exchange interaction α2J. By varying spin values and interaction strengths, we determine the exact energy eigenstates that are used to determine closed-form analytic solutions for the heat capacity and magnetic susceptibility of the system and further analyze the evolution of the properties of the system based on the parameter values chosen. Furthermore, this study shows that the Schottky anomaly shifts towards zero as the ground-state of the system approaches a quantum phase transition between spin states. Additionally, we investigate the development of phase transitions produced by the convergence of the Schottky anomaly with both variable exchange interactions and external magnetic field.

EXACT SOLUTIONS IN A SPATIALLY ANISOTROPIC QUANTUM SPIN LADDER MODEL HAVING TWO- AND FOUR-SPIN EXCHANGE INTERACTIONS

2009 ◽  
Vol 23 (08) ◽  
pp. 1981-2019 ◽  
Author(s):  
J. H. BARRY ◽  
J. D. COHEN ◽  
M. W. MEISEL
Keyword(s):  
Spin Exchange ◽  
Inelastic Neutron Scattering ◽  
Exchange Interactions ◽  
Inelastic Neutron ◽  
Elementary Excitation ◽  
Quantum Spin ◽  
Quantum Model ◽  
Spin Ladder ◽  
Zero Field ◽  
Ladder Model

We consider a two-leg S=1/2 quantum spin ladder model with two-spin (intra-rung) and four-spin (inter-rung) Heisenberg exchange interactions and a uniform magnetic field. Exact mappings are derived connecting the partition function and correlations in the three-parameter quantum model to those known in a two-parameter Ising chain. The quantum phase diagram of the ladder magnet is determined. Static correlations provide pertinent correlation lengths and underlie spatial fluctuation behaviors at arbitrary temperatures, including quantum fluctuations at absolute zero. Dynamic correlations in zero field are used to obtain an exact solution for the inelastic neutron scattering function Sxx(q, ω) at all temperatures, explicitly yielding the elementary excitation spectrum.

scholarly journals Pressure-induced normal-incommensurate-commensurate phase transitions in TiPO4

2014 ◽  
Vol 70 (a1) ◽  
pp. C263-C263 ◽  
Author(s):  
Maxim Bykov ◽  
Elena Bykova ◽  
Leonid Dubrovinsky ◽  
Michael Hanfland ◽  
Hanns-Peter Liermann ◽  
...  
Keyword(s):  
High Pressure ◽  
Phase Transitions ◽  
Degrees Of Freedom ◽  
Spin Exchange ◽  
Exchange Interactions ◽  
Quantum Spin ◽  
Singlet Ground State ◽  
Transition Temperatures ◽  
Spin Lattice ◽  
Commensurate Phase

The complex interplay between spin, charge, orbital, and lattice degrees of freedom has made low-dimensional quantum spin magnets with strong antiferromagnetic (AF) spin-exchange coupling prime candidates for studying unusual magnetic phenomena. A progressive spin-lattice dimerization in one-dimensional AF Heisenberg chains, which occurs below a critical temperature and induces a singlet ground state with a magnetic gap, is commonly referred to as spin-Peierls (SP) transition. Recently, the compounds TiOX (X = Cl, Br) and TiPO4have been intensively investigated due to their unconventional behavior [1,2]. Unlike standard SP systems, TiOX and TiPO4undergo a sequence of normal-incommensurate-commensurate phase transitions on cooling at remarkably high transition temperatures. The transition temperatures are related to the direct exchange interactions between Ti ions, which increases strongly with decreasing the distance between the Ti ions, and therefore is very sensitive to the applied hydrostatic pressure. We have performed pressure-dependent single-crystal X-ray diffraction of TiPO4using synchrotron radiation. TiPO4undergoes a pressure-induced pahse transiton towards an incommensurate phase already below 10 GPa. This transformation is followed by the lock-in phase transition to the dimerized SP phase. Both structures are analogous to those at low temperatures, but reveal significantly larger modulation amplitudes. In this contribution we will present the detailed discussion of the high-pressure structures of TiPO4and their behavior on compression. Furthermore, similarities and differences of high-pressure phase diagrams of TiOCl and TiPO4and discrepancies between predicted and observed structures will be considered.

scholarly journals Thermodynamics and Magnetic Excitations in Quantum Spin Trimers: Applications for the Understanding of Molecular Magnets

Crystals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 93 ◽  
Author(s):  
Amelia Brumfield ◽  
Jason Haraldsen
Keyword(s):  
Spin Exchange ◽  
Inelastic Neutron Scattering ◽  
Inelastic Neutron ◽  
Quantum Spin ◽  
Molecular Magnets ◽  
Molecular Magnet ◽  
Magnetic Excitations ◽  
Structure Factors ◽  
Coupling Parameters ◽  
The Individual

Molecular magnets provide a playground of interesting phenomena and interactions that have direct applications for quantum computation and magnetic systems. A general understanding of the underlying geometries for molecular magnets therefore generates a consistent foundation for which further analysis and understanding can be established. Using a Heisenberg spin-spin exchange Hamiltonian, we investigate the evolution of magnetic excitations and thermodynamics of quantum spin isosceles trimers (two sides J and one side α J ) with increasing spin. For the thermodynamics, we produce exact general solutions for the energy eigenstates and spin decomposition, which can be used to determine the heat capacity and magnetic susceptibility quickly. We show how the thermodynamic properties change with α coupling parameters and how the underlying ground state governs the Schottky anomaly. Furthermore, we investigate the microscopic excitations by examining the inelastic neutron scattering excitations and structure factors. Here, we illustrate how the individual dimer subgeometry governs the ability for probing underlying excitations. Overall, we feel these calculations can help with the general analysis and characterization of molecular magnet systems.

scholarly journals Probing resonating valence bond states in artificial quantum magnets

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Kai Yang ◽  
Soo-Hyon Phark ◽  
Yujeong Bae ◽  
Taner Esat ◽  
Philip Willke ◽  
...  
Keyword(s):  
Quantum Information Processing ◽  
Energy Levels ◽  
Finite Size ◽  
Valence Bond ◽  
Exchange Interactions ◽  
Atomic Scale ◽  
Scanning Tunneling ◽  
Many Body ◽  
Quantum Magnets ◽  
Resonating Valence Bond

AbstractDesigning and characterizing the many-body behaviors of quantum materials represents a prominent challenge for understanding strongly correlated physics and quantum information processing. We constructed artificial quantum magnets on a surface by using spin-1/2 atoms in a scanning tunneling microscope (STM). These coupled spins feature strong quantum fluctuations due to antiferromagnetic exchange interactions between neighboring atoms. To characterize the resulting collective magnetic states and their energy levels, we performed electron spin resonance on individual atoms within each quantum magnet. This gives atomic-scale access to properties of the exotic quantum many-body states, such as a finite-size realization of a resonating valence bond state. The tunable atomic-scale magnetic field from the STM tip allows us to further characterize and engineer the quantum states. These results open a new avenue to designing and exploring quantum magnets at the atomic scale for applications in spintronics and quantum simulations.

scholarly journals T − W relation and free energy of the Heisenberg chain at a finite temperature

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Pengcheng Lu ◽  
Yi Qiao ◽  
Junpeng Cao ◽  
Wen-Li Yang ◽  
Kang jie Shi ◽  
...  
Keyword(s):  
Free Energy ◽  
Spin Chain ◽  
Quantum Spin ◽  
Heisenberg Chain ◽  
Quantum Spin Chain ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Lattice Quantum ◽  
Quantum Integrable Models ◽  
Invariant Quantum

Abstract A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t − W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corre- sponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.

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