PI: Ribhu Kaul
Affiliation: University of Kentucky Job Title: Assistant Professor

The main research direction for which we have made use of HPC resources in the simulations of the quantum mechanics of model many-body Hamiltonians. Although traditionally our group has worked on spin models, recent studies have turned to the properties of systems with fermions as well. Generally we are interested in exotic phases and phase transition that can occur in these model systems. Beyond the conceptual interest in these fundamental problems, we are also interested in finding various experimental systems ranging from complex materials to ultra-cold atoms in optical lattices that realize such exotic many body behavior.

Here is a list of projects being pursues currently, as of August 2014 under my supervision that use the HPC facilities in UK. In addition we have at least two large allocations on external national facilities using the XSEDE program of the NSF.

Electronic Structure of Thin Films and Bulk Single Crystal of Iridates:

Understanding structural distortion and their role in crystal field effects in strongly correlated transition metal oxide materials.

Students:

Tom Pace

Ahmed Khalifa, Graduate, Added on MCC cluster, 04/13/2022

Search for exotic quantum phases of spins on the diamond lattice

We are investigating the phases of SU(N) quantum spins on the diamond lattice through unbiased quantum Monte Carlo simulations. Particular questions we are interested in are the nature of the non-magnetic phases and the critical points that separate these phases from the magnetic phase in three dimensions.

Students

Nisheeta Desai, Grad

Quantum Spin Liquid in Triangular Anti-ferromagnets

Lead Researcher: Ribhu Kaul, (Associate Professor, University of Kentucky) I am investigating the phase transitions between nematic phases and valence bond solids on non-bipartite lattices. Interestingly, I have found that in between these two phases there emerges an exotic quantum spin liquid phase. Current studies are focuses on understanding the nature of this phase and the critical points that separate this phase from more conventional phases.

Spin-1 magnets on a percolating cluster

Lead Junior Researcher: Simon Lovell (post-bac, University of Kentucky) We are investigating the percolation transition that occurs for a spin-1 Heisenberg model with biquadratic interactions on a diluted triangular lattice. The objective is to learn if the order-disorder transition is driven by site dilution (classically) or by quantum fluctuations. The computational method used in this project is the stochastic series expansion quantum Monte Carlo algorithm. The simulations will be preformed on the supercomputing clusters at the University of Kentucky.

Students

Simon Lovell, Post-doc

Critical points in SU(N) magnets

Lead Junior Researcher: Matt Block, (post-doc, University of Kentucky)
We are currently pursuing two computational projects using high-performance supercomputers. First, we are exploring the phase diagram of a nearest-neighbor antiferromagnetic SU(N) model on the kagome lattice as a function of N. We also augment the model with interactions that allow for continuous tuning from magnetic to paramagnetic phases. Second, we are investigating the continuity of the Néel-VBS phase transition on the rectangular (anisotropic nearest neighbor) SU(2) JQ model (Heisenberg plus plaquette interaction) as the isotopic limit is approached.

Student

Matt Block, Post-doc

Quantum criticality in 2D magnets with "easy-plane" anisotropy

Lead Junior Researcher: Jon Demidio, (grad student, University of Kentucky)
Description: In this project we investigate the properties of a quantum phase transition that exists for our microscopic lattice model, which is symmetric under an "easy-plane" subgroup of SU(N). We find that this model exhibits two distinct quantum phases of matter: one where the spins are magnetically ordered along the direction of the easy-plane, and one where the spins lose magnetic order, but form a crystalline pattern of non-magnetic dimers along the lattice. We investigate the transition which exists between these two phases, which is predicted to violate the conventional description of quantum phase transitions.

Student

Jon Demidio, Grad

Designing SU(N) quantum spin Hamiltonians

Currently, I am carrying out a systematic study of models of anti-‐ferromagnets that do not suffer from the sign problem. This involves both algorithmic development and the use of large scale computational resources. The codes I will use are written by me in C++.

Entanglement in one-dimensional quantum spin systems

The aim of this project is to use entanglement as a means of characterizing strongly correlated quantum spin systems. Entanglement in the context of a 1 dimensional spin chain means the following: "Given a linear chain of interacting quantum spins, how much information is shared between a portion (sub-‐system) of the chain and its compliment?" It is a well known fact that the entanglement as a function of sub-‐ system size has a "universal" scaling form, meaning that the form remains the same regardless of the spin model that one is considering. Though the basic form remains the same, certain numerical constants will vary from model to model. It is these constants which offer a complete characterization of the spin model in question.

Furthermore, it is these constants that one can directly measure in experiments with real materials and therefore establish a link between real physical systems and models which effectively describe them.

Quantum systems in any dimension are equivalent to classical systems in one higher dimension, thus our 1 dimensional quantum spin chains require 2 dimensional simulation cells. The other dimension plays the role of inverse temperature (lower temperature, bigger size). We are interested in purely quantum effects which occur at very low temperatures thus our simulation cells can be quite large (around 100x100,000 units, where the first is the number of spins and the second is the number of units in the inverse temperature direction). We use Monte Carlo techniques to probabilistically sample the entire space of allowed configurations. A non-‐local updating scheme allows for efficient sampling of the vast number of configurations. Measuring the entanglement requires independently sampling several copies (usually 2) of a 2 dimensional cell and joining the configurations (cells) together or splitting them apart whenever spins match each other in a particular region. The code was developed in C++ by our group, needing functions only from the standard template library. The main code generates data which is analyzed by several Python scripts, which often require NUMPY.

Students:

Graduate student - Jonathan D'Emidio
Postdoc - Matthew Block.
Postdoc - Julia S Wildeboer

Generalized Heisenberg N-flavor Projector Model on the Kagome Lattice

Using a generalization of the Heisenberg operator to N flavors, the so-‐called projector operator, on the non-‐bipartite Kagome lattice we study the ground state phases of the model as N is varied. For small N, the phase is well-‐known to be an analog of antiferromagnetic order. For large N, it is believed that some valence bond solid (VBS) ordered phase takes root. Our first question in this investigation is to determine if there exists a spin-‐liquid phase for some intermediate value or values of N. A second question is to identify the VBS pattern or patterns that show up for large N. We can, in addition, add terms to our model that will drive magnetic or VBS order with a continuously variable parameter. This will allow for a systematic and detailed study of the phase transition between the two conventional phases for each value of N. For those transitions that prove to be continuous, we can further analyze the properties of the transition with the possibility of some novel critical behavior being observed. To these ends, we will consider several values of N and a substantial number of system sizes to facilitate robust finite-‐size scaling. The measurements for this model will be performed numerically using home-‐grown C++ codes implementing a specialized version of the stochastic series expansion quantum Monte Carlo method. Data analysis is performed using Python scripts for conventional error analysis and plotting.

Students:

Postdoc - Matt Block

The structure factor of the classical FCC nearest neighbor model

The face centered cubic lattice with anti-‐ferromagnetic classical interactions has a phase transition at low temperatures. However, the way in which the lattice orders is unclear. The structure factor, which describes how the lattice orders in the ground states has been measured for smaller lattices, but larger lattices are needed to remove the finite-‐size effects that dominate these measurements. The approach of this project is to use graphics processing units to run classical Monte Carlo simulations for large lattices by making measurements and updates of lattice sites in parallel. A C program is being written with the CUDA libraries to simulate these lattices on GPUs. The program takes the lattice shape and interaction from input so lattices with different structures and interaction models can be studied simply by changing the input file. Python scripts are being used to generate the input files, analyze the output files, and to make plots.

Students:

Undergraduate student - Forrest Simmons

Collaborators:

Simon Lovell, UKY, UGrad
Forrest Simmons, UKY, UGrad
Jon Demidio, UKY, Grad
Sumiran Pujari, UKY, Postdoc
Prof. Anders Sandvik, Boston University
Prof. Roger Melko, Boston University
Thomas Lang, Boston University, Postdoc

Completed Projects:

As of March 02, 2016

Quantum Spin Liquid in Triangular Anti-ferromagnets

Spin nematics, valence-bond solids and spin liquids in SO($N$) quantum spin models on the triangular lattice Ribhu K. Kaul Journal-ref: Phys. Rev. Lett. 115, 157202 (2015)

Quantum criticality in 2D magnets with "easy-plane" anisotropy

First-order superfluid to valence bond solid phase transitions in easy-plane SU($N$) magnets for small-$N$ Jonathan D'Emidio, Ribhu K. Kaul Journal-ref: Phys. Rev. B 93, 054406 (2016)

Entanglement in one-¬dimensional quantum spin systems

Rényi entanglement entropy of critical SU($N$) spin chains Jonathan D'Emidio, Matthew S. Block, Ribhu K. Kaul
Journal-ref: Phys. Rev. B 92, 054411 (2015)

Critical points in SU(N) magnets

Numerical studies of various Neel-VBS transitions in SU(N) anti-ferromagnets Ribhu K. Kaul, Matthew Block Journal-ref: J. Phys.: Conf. Ser. 640 012041 (2015)

Designing SU(N) quantum spin Hamiltonians

Marshall-positive SU($N$) quantum spin systems and classical loop models: A practical strategy to design sign-problem-free spin Hamiltonians Ribhu K. Kaul Journal-ref: Phys. Rev. B 91, 054413 (2015)

Published work from supercomputers at UKY:

2016

Quantum criticality in 2D magnets with "easy-plane" anisotropy First-order superfluid to valence bond solid phase transitions in easy-plane SU($N$) magnets for small-$N$ Jonathan D'Emidio, Ribhu K. Kaul Journal-ref: Phys. Rev. B 93, 054406 (2016)

2015

Quantum Spin Liquid in Triangular Anti-ferromagnets Spin nematics, valence-bond solids and spin liquids in SO($N$) quantum spin models on the triangular lattice Ribhu K. Kaul Journal-ref: Phys. Rev. Lett. 115, 157202 (2015)
textEntanglement in one-¬dimensional quantum spin systems Rényi entanglement entropy of critical SU($N$) spin chains Jonathan D'Emidio, Matthew S. Block, Ribhu K. Kaul Journal-ref: Phys. Rev. B 92, 054411 (2015)
textCritical points in SU(N) magnets Numerical studies of various Neel-VBS transitions in SU(N) anti-ferromagnets Ribhu K. Kaul, Matthew Block Journal-ref: J. Phys.: Conf. Ser. 640 012041 (2015)
textDesigning SU(N) quantum spin Hamiltonians Marshall-positive SU($N$) quantum spin systems and classical loop models: A practical strategy to design sign-problem-free spin Hamiltonians Ribhu K. Kaul Journal-ref: Phys. Rev. B 91, 054413 (2015)

2014

G. Murthy, and R. K. Kaul Phys. Rev. Lett. 112, 056402 (2014) http://dx.doi.org/10.1103/PhysRevLett.112.056402 http://arxiv.org/abs/1307.2212

2013

“Fate of CPN−1 fixed points with q-monopoles” Matthew S. Block, Roger G. Melko and Ribhu K. Kaul. Phys. Rev. Lett. 111, 137202 (2013) http://prl.aps.org/abstract/PRL/v111/i13/e137202 http://arxiv.org/abs/1307.0519
“Evolution of magnetism in the single-crystal honeycomb iridates (Na1−xLix)2IrO3” G. Cao, T. F. Qi, L. Li, J. Terzic, S. J. Yuan, M. Tovar, G. Murthy and R. K. Kaul Phys. Rev. B 88, 220414(R) (2013) http://dx.doi.org/10.1103/PhysRevB.88.220414 http://arxiv.org/abs/1307.2212
“Designer Hamiltonians: bridging lattice-scale physics and continuum field theory with quan- tum Monte Carlo simulations” Ribhu K. Kaul, Roger G. Melko and Anders W. Sandvik. Annu. Rev. Con. Mat. Phys. 4, 179 (2013) http://www.annualreviews.org/doi/abs/10.1146/annurev-‐conmatphys-‐030212-‐ 184215 http://arxiv.org/abs/1204.5405

2012

“Spin-orbit tuned metal-insulator transitions in single-crystal Sr2Ir1−xRhxO4 (0 ≤ x ≤ 1)” T. F. Qi, O. B. Korneta, L. Li, K. Butrouna, V. S. Cao, Xiangang Wan, P. Schlottmann, R. K. Kaul and G. Cao. Phys. Rev. B 86, 125105 (2012) http://prb.aps.org/abstract/PRB/v86/i12/e125105 http://arxiv.org/abs/1207.1714
“Metals get an awkward cousin” Ribhu K. Kaul. Physics 5, 82 (2012) http://physics.aps.org/articles/v5/82 http://arxiv.org/abs/1207.5549
“Spin nematic ground state of the triangular lattice S=1 biquadratic model” Ribhu K. Kaul. Phys. Rev. B 86, 104411 (2012) http://prb.aps.org/abstract/PRB/v86/i10/e104411 http://arxiv.org/abs/1208.4133
“Lattice model for the SU(N) Neel-‐VBS quantum phase transition at large N ” Ribhu K. Kaul and Anders W. Sandvik. Phys. Rev. Lett. 108 137201, (2012). http://prl.aps.org/abstract/PRL/v108/i13/e137201 http://arxiv.org/abs/1110.4130
“Quantum phase transitions in bilayer SU(N) anti-ferromagnets” Ribhu K. Kaul. Phys. Rev. B 85, 180411(R) (2012). http://prb.aps.org/abstract/PRB/v85/i18/e180411 http://arxiv.org/abs/1203.6677
“The N ́eel-VBS transition in three-dimensional antiferromagnets” Matthew S. Block and Ribhu K. Kaul. Phys. Rev. B 86, 134408 (2012) http://prb.aps.org/abstract/PRB/v86/i13/e134408 http://arxiv.org/abs/1205.3530

2011

“Quantum criticality in SU(3) and SU(4) anti-ferromagnets” Ribhu K. Kaul. Phys. Rev. B 84 054407, (2011). http://prb.aps.org/abstract/PRB/v84/i5/e054407 http://arxiv.org/abs/1010.1937

Grants funded through DLX usage:

Kaul Ribhu DMR-1056536 Restricted Scope for Participant Support: CAREER: Novel States of Correlated Quantum Matter in Numerical Simulations, Field Theories and Natural Systems National Science Foundation 9/1/2011 - 8/31/2016 SCOPE
Kaul Ribhu DMR-1056536 CAREER: Novel States of Correlated Quantum Matter in Numerical Simulations, Field Theories and Natural Systems National Science Foundation 9/1/2011 - 8/31/2016 $380,000
Kaul, Ribhu DMR-1056536 CAREER: Novel States of Correlated Quantum Matter in Numerical Simulations, Field Theories and Natural Systems $285,000 National Science Foundation 9/1/2011 8/31/2016
1 NSF CAREER award “Novel states of correlated quantum matter in numerical simula-‐ tions, field theories and natural systems”.
2 ORNL’s Ralph Powe Junior Faculty award “Novel phenomena in quantum magnets with strong spin-‐orbit coupling”
3 Co-‐PI on NSF award “Holography, Supersymmetry, and Numerics in Quantum Critical and Quantum Lifshitz Theories” with G. Murthy (PI), S. Das(co-‐PI) and A. Shapere(co-‐PI).

Electronic Structure of Thin Films and Bulk Single Crystal of Iridates:

Students:

Search for exotic quantum phases of spins on the diamond lattice

Students

Quantum Spin Liquid in Triangular Anti-ferromagnets

Spin-1 magnets on a percolating cluster

Students

Critical points in SU(N) magnets

Student

Quantum criticality in 2D magnets with "easy-plane" anisotropy

Student

Designing SU(N) quantum spin Hamiltonians

Entanglement in one-­dimensional quantum spin systems

Students:

Generalized Heisenberg N-­flavor Projector Model on the Kagome Lattice

Students:

The structure factor of the classical FCC nearest neighbor model

Students:

Collaborators:

Completed Projects:

Quantum Spin Liquid in Triangular Anti-ferromagnets

Quantum criticality in 2D magnets with "easy-plane" anisotropy

Entanglement in one-¬dimensional quantum spin systems

Critical points in SU(N) magnets

Designing SU(N) quantum spin Hamiltonians

Published work from supercomputers at UKY:

2016

2015

2014

2013

2012

2011

Grants funded through DLX usage:

Entanglement in one-dimensional quantum spin systems

Generalized Heisenberg N-flavor Projector Model on the Kagome Lattice

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