Imperfections in correlated materials can alter their ground state as well as finite-temperature properties in significant ways. Here, we develop a method based on numerical linked-cluster expansions for calculating exact finite-temperature properties of disordered lattice models directly in the thermodynamic limit. We show that a continuous distribution for disordered parameters can be achieved using a set of carefully chosen discrete modes in the distribution, which allows for the averaging of properties over all disorder realizations. We benchmark our results for thermodynamic properties of the square-lattice Ising and quantum Heisenberg models with bond disorder against Monte Carlo simulations and study them as the strength of disorder changes. We also apply the method to the disordered Heisenberg model on the frustrated checkerboard lattice, which is closely connected to ${\mathrm{Sr}}_{2}\mathrm{Cu}({\mathrm{Te}}_{0.5}{\mathrm{W}}_{0.5}){\mathrm{O}}_{6}$ . Our method can be used to study finite-temperature properties of other disordered quantum lattice models, including those for interacting lattice fermions.Imperfections in correlated materials can alter their ground state as well as finite-temperature properties in significant ways. Here, we develop a method based on numerical linked-cluster expansions for calculating exact finite-temperature properties of disordered lattice models directly in the thermodynamic limit. We show that a continuous distribution for disordered parameters can be achieved using a set of carefully chosen discrete modes in the distribution, which allows for the averaging of properties over all disorder realizations. We benchmark our results for thermodynamic properties of the square-lattice Ising and quantum Heisenberg models with bond disorder against Monte Carlo simulations and study them as the strength of disorder changes. We also apply the method to the disordered Heisenberg model on the frustrated checkerboard lattice, which is closely connected to ${\mathrm{Sr}}_{2}\mathrm{Cu}({\mathrm{Te}}_{0.5}{\mathrm{W}}_{0.5}){\mathrm{O}}_{6}$. Our method can be used to study finite-temperature properties of other disordered quantum lattice models, including those for interacting lattice fermions.

arXiv:1810.12901Physical review. B./Physical review. BMay 10, 20198 citations

Thermodynamics of a frustrated quantum magnet on a square lattice

Vivek Kumar Bhartiya, Kirill Yu. Povarov, Zewu Yan +1 more

Bulletin of the American Physical SocietyMar 7, 20190 citations

Ground-State Properties of the Frustrated One-Dimensional S=1 Heisenberg Model

Takashi Tonegawa, Makoto Kaburagi, Noriya Ichikawa +1 more

Springer proceedings in physicsJan 1, 19920 citations

Ising-type critical exponents of the fully frustrated spin-1/2 Heisenberg FM/AF square bilayer at a critical magnetic field

Katarína Karľová, Jozef Strečka

The fully frustrated spin-1/2 Heisenberg FM/AF square bilayer in a magnetic field with the ferromagnetic inter-dimer interaction and the antiferromagnetic intra-dimer interaction is explored by the use of localized many-magnon approach, which allows to connect the original purely quantum Heisenberg spin model on a square bilayer with the effective ferromagnetic Ising model on a simple square lattice. Magnetization and specific heat are investigated exactly at a field-driven phase transition from the singlet-dimer phase towards the fully saturated ferromagnetic phase, which changes from a discontinuous phase transition to a continuous one at a certain critical temperature. The mapping correspondence between the spin-1/2 Heisenberg FM/AF square bilayer and the ferromagnetic Ising square lattice suggests for this special critical point of the spin-1/2 Heisenberg FM/AF square bilayer critical exponents from the standard two-dimensional Ising universality class.The fully frustrated spin-1/2 Heisenberg FM/AF square bilayer in a magnetic field with the ferromagnetic inter-dimer interaction and the antiferromagnetic intra-dimer interaction is explored by the use of localized many-magnon approach, which allows to connect the original purely quantum Heisenberg spin model on a square bilayer with the effective ferromagnetic Ising model on a simple square lattice. Magnetization and specific heat are investigated exactly at a field-driven phase transition from the singlet-dimer phase towards the fully saturated ferromagnetic phase, which changes from a discontinuous phase transition to a continuous one at a certain critical temperature. The mapping correspondence between the spin-1/2 Heisenberg FM/AF square bilayer and the ferromagnetic Ising square lattice suggests for this special critical point of the spin-1/2 Heisenberg FM/AF square bilayer critical exponents from the standard two-dimensional Ising universality class.

Phase TransitionsFeb 7, 20191 citation

Quantum Heisenberg antiferromagnet on low-dimensional frustrated lattices

Oleg Derzhko, Taras Krokhmalskii, Johannes Richter

arXiv:1103.5124Theoretical and Mathematical PhysicsSep 1, 20116 citations

Finite-temperature order-disorder phase transition in a frustrated bilayer quantum Heisenberg antiferromagnet in strong magnetic fields

Johannes Richter, Oleg Derzhko, Taras Krokhmalskii

We investigate the thermodynamic properties of the frustrated bilayer quantum Heisenberg antiferromagnet at low temperatures in the vicinity of the saturation magnetic field. The low-energy degrees of freedom of the spin model are mapped onto a hard-square gas on a square lattice. We use exact diagonalization data for finite spin systems to check the validity of such a description. Using a classical Monte Carlo method we give a quantitative description of the thermodynamics of the spin model at low temperatures around the saturation field. The main peculiarity of the considered two-dimensional Heisenberg antiferromagnet is related to a phase transition of the hard-square model on the square lattice, which belongs to the two-dimensional Ising model universality class. It manifests itself in a logarithmic (low-) temperature singularity of the specific heat of the spin system observed for magnetic fields just below the saturation field.We investigate the thermodynamic properties of the frustrated bilayer quantum Heisenberg antiferromagnet at low temperatures in the vicinity of the saturation magnetic field. The low-energy degrees of freedom of the spin model are mapped onto a hard-square gas on a square lattice. We use exact diagonalization data for finite spin systems to check the validity of such a description. Using a classical Monte Carlo method we give a quantitative description of the thermodynamics of the spin model at low temperatures around the saturation field. The main peculiarity of the considered two-dimensional Heisenberg antiferromagnet is related to a phase transition of the hard-square model on the square lattice, which belongs to the two-dimensional Ising model universality class. It manifests itself in a logarithmic (low-) temperature singularity of the specific heat of the spin system observed for magnetic fields just below the saturation field.

arXiv:cond-mat/0606806Physical Review BOct 27, 200641 citations

{\mathrm{Sr}}_{2}\mathrm{Cu}({\mathrm{Te}}_{0.5}{\mathrm{W}}_{0.5}){\mathrm{O}}_{6}

. Our method can be used to study finite-temperature properties of other disordered quantum lattice models, including those for interacting lattice fermions.