Finite and infinite matrix product states for Gutzwiller projected mean-field wavefunctions and their applications to quantum spin systems

Petrica, Gabriel

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https://hdl.handle.net/2142/112948 Copy

Description

Title

Finite and infinite matrix product states for Gutzwiller projected mean-field wavefunctions and their applications to quantum spin systems

Author(s)

Petrica, Gabriel

Issue Date

2021-05-19

Director of Research (if dissertation) or Advisor (if thesis)

Clark, Bryan K

Doctoral Committee Chair(s)

Stone, Michael

Committee Member(s)

• Cooper, Lance S
• Faulkner, Thomas

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• matrix product states
• Gutzwiller projection
• mean-field groundstates
• entanglement spectrum
• entanglement entropy
• quantum spin liquids
• topological order

Abstract

Modeling and understanding magnetically disordered ground states of 2D or quasi-2D quantum spin systems has been an important research theme in recent years. Many of these states show exotic quantum orders that cannot be understood in the context of Landau-Ginzburg order parameters. With few exceptions, 2D analytical calculations are not well controlled. Therefore, numerical procedures are essential to test theories and analytical calculations. Moreover, efficient numerical procedures can be used in their own right for exploration and discovery, guiding analytical and experimental work. Chapter 1 introduces Gutzwiller projected slave-fermion wavefunctions as variational wavefunctions used to investigate quantum spin systems. We further briefly discuss matrix product states as efficient representations of gapped quantum wavefunctions which are intimately related to the entanglement properties of these wavefunctions. We also present known results concerning the detection of exotic quantum orders from measures of many-body entanglement. In Chapter 2 we review the mathematical background of mean-field fermionic states, matrix product states (MPS), and quantum entanglement. Furthermore, some novel algorithms are also outlined. In Chapter 3 we present our original contribution, a novel method to obtain both the finite and infinite MPS (iMPS) representation of the ground state of an arbitrary fermionic quadratic mean-field Hamiltonian,(which in the simplest case is a Slater determinant and in the most general case is a Pfaffian). We also show how to represent products of such states (e.g. determinants times Pfaffians). Gutzwiller projection is trivially realized for the MPS representations of the mean-field groundstates. We also develop a novel approach that can find an orthonormal basis in the thermodynamic limit in case of degeneracy in the ground state manifold. We then benchmark our method by obtaining the MPS and iMPS representation of Gutzwiller projected mean-field states that arise from the variational slave-fermion approach to theS= 1 bilinear-biquadratic(BLBQ) quantum spin chain. We find the energies of the MPS and iMPS states match the variational energies closely indicating the method is accurate and there is minimal loss due to truncation error. We then present the exploration of the entanglement spectra of projected slave-fermion states exploring their qualitative features and finding good qualitative agreement with the respective exact ground state spectra found from the density-matrix renormalization group. Chapter 4 provides a summary of our work and contains a discussion of future directions.

Graduation Semester

2021-08

Type of Resource

Thesis

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http://hdl.handle.net/2142/112948

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Copyright 2021 Gabriel Petrica

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