- Postdoctoral Positions, University of Illinois at Urbana-Champaign; Oppenheimer fellow at LANL
- Ph.D., Swiss Federal Institute of Technology, 1987
- M.S., Instituto Balseiro, Bariloche, 1987

## Gerardo Ortiz

Professor, Physics

Professor, Physics

- ortizg@indiana.edu
- (812) 855-0367
- Swain West 230
- Office Hours

- Postdoctoral Positions, University of Illinois at Urbana-Champaign; Oppenheimer fellow at LANL
- Ph.D., Swiss Federal Institute of Technology, 1987
- M.S., Instituto Balseiro, Bariloche, 1987

condensed matter physics (theoretical)

A great challenge of theoretical physics is understanding and modeling interacting quantum many-body systems or quantum fields, and accurately predicting properties and functionalities of matter from the fundamental laws of quantum mechanics. My research work is in condensed matter physics and quantum information science.

One of my main interests centers on the physics of strongly coupled systems, which is one of today's most active research areas in condensed matter. These systems happened to be strongly correlated since no obvious small coupling constant exists, and consequently exhibit high sensitivity to small parameter changes. My interest is fueled by the new states of matter such systems can display and the exceptional material properties these phases sometimes exhibit. The physics of high temperature superconducting materials, lanthanide and actinide materials (often referred to as f-electron materials), quantum Hall systems, etc. are cases in point. Indeed, the multiplicity of distinct and novel quantum phases observed experimentally confront us with new paradigms that challenge our understanding of the fundamental principles behind such complex phenomena. For example, whether the mechanism controlling the coexistence and/or competition between magnetism and superconductivity (or Bose-Einstein condensation) has the same physical origin in different classes of materials is still an open question. This complex phenomena exhibited by Nature exceeds our ability to explain them, in part, because of a lack of appropriate mathematical tools to disentangle its mysteries. From the theoretical viewpoint the hurdle is in the presence of non-linear couplings, non-perturbative phenomena, and a panoply of competing quantum orders. As a result, all possible phases of matter and their transitions cannot (even approximately) be described within Landau's framework and new physics concepts such as topological quantum order emerge.

The quest to explore the ultimate limits and principles of quantum physics is out there. Quantum technologies are no longer a theorist's dream. For example, commercial quantum cryptography devices have become available. I am interested in studying foundational, software, and hardware aspects of quantum computation and information. Because of the exciting recent development of new algorithms, such as Shor's factoring and Grover's quantum search, that solve difficult problems on a quantum computer using algorithms that would be impractical on a classical computer, it is easy to overlook the fact that Feynman's original proposal for quantum computers was for the purpose of solving quantum physics problems. Simulation of physical phenomena using quantum devices is one of my areas of research. I am also concerned with topics of potential overlap between my two research disciplines, where feedback from one field may help to resolve significant problems in the other. After all, a quantum computer is a quantum many-body system. What are the concepts from quantum information that one can use to study or predict phenomena in condensed matter physics? Similarly, what concepts can be borrowed from condensed matter to quantify measures of information? These are fundamental open questions. Designing and building a quantum computer or a quantum simulator is a ultimate example of topics that meet the boundaries of both disciplines. Cold atom physics is another.

"Elements of Phase Transitions and Critical Phenomena", H. Nishimori and G. Ortiz (Oxford University Press, Oxford, 2010).

"Superconductivity in strongly repulsive fermions: The role of kinetic-energy frustration", L. Isaev, G. Ortiz, and C. D. Batista, *Phys. Rev. Lett.* (in press).

"Unified approach to quantum and classical dualities", E. Cobanera, G. Ortiz, and Z. Nussinov, *Phys. Rev. Lett.* 104, 020402 (2010).

"Field-induced orbital antiferromagnetism in Mott insulators", K. A. Al-Hassanieh, C. D. Batista, G. Ortiz, and L. N. Boulaevskii, *Phys. Rev. Lett.* 103, 216402 (2009).

"Local physics of magnetization plateaux in the Shastry-Sutherland model", L. Isaev, G. Ortiz, and J. Dukelsky, *Phys. Rev. Lett* 103, 177201 (2009).

"Breached pairing in trapped three-color atomic Fermi gases", B. Errea, J. Dukelsky, and G. Ortiz, *Phys. Rev.* A (Rapid Communications) 79, 051603 (2009).

"Ferrotoroidic moment as a quantum geometric phase", C. D. Batista, G. Ortiz, and A. A. Aligia, *Phys. Rev. Lett.* 101, 077203 (2008).

"A symmetry principle for topological quantum order", Z. Nussinov and G. Ortiz, Ann. *Phys.* (NY) 324, 977 (2009).

"Autocorrelations and thermal fragility of anyonic loops in topologically quantum ordered systems", Z. Nussinov and G. Ortiz, *Phys. Rev.* B 77, 064302 (2008).

"Integrable models for asymmetric Fermi superfluids: Emergence of a new exotic pairing phase", J. Dukelsky, G. Ortiz, S. Rombouts, and van Houcke, *Phys. Rev. Lett.* 96, 180404 (2006).

"BCS-to-BEC crossover from the exact BCS solution", G. Ortiz and J. Dukelsky, *Phys. Rev.* A 72, 043611 (2005).

"Algebraic approach to interacting quantum systems", C.D. Batista and G. Ortiz, *Adv. in Phys.* 53, 1 (2004).

"Unveiling order behind complexity: Ferromagnetism and Bose-Einstein condensation", C.D. Batista, G. Ortiz, and J.E. Gubernatis, *Phys. Rev.* B (Rapid Communications) 65, 180402 (2002).

"Generalized Jordan-Wigner transformations", C.D. Batista and G. Ortiz, *Phys. Rev. Lett.* 86, 1082 (2001).

"Unified description of the resonance peak and incommensuration in high-Tc superconductors", C.D. Batista, G. Ortiz, and A.V. Balatsky, *Phys. Rev.* B 64, 172508 (2001).

"Quantum phase diagram of the t-Jz chain model", C.D. Batista and G. Ortiz, *Phys. Rev. Lett.* 85, 4755 (2000).

"Inhomogeneity-Induced Superconductivity?", J. Eroles, G. Ortiz, A.V. Balatsky, and A.R. Bishop, *Europhys. Lett.* 50, 540 (2000).

"Quantum-mechanical position operator and localization in extended systems", A.A. Aligia and G. Ortiz, *Phys. Rev. Lett.* 82, 2560 (1999).

"Zero temperature phases of the electron gas", G. Ortiz, M. Harris, and P. Ballone, *Phys. Rev. Lett.* 82, 5317 (1999).

"Exchange-correlation hole in polarized insulators: implications for the microscopic functional theory of dielectrics", G. Ortiz, I. Souza, and R.M. Martin, *Phys. Rev. Lett.* 80, 353 (1998).

"Functional theory of extended Coulomb systems", R.M. Martin and G. Ortiz, *Phys. Rev.* B 56, 1124 (1997).

"Correlation energy, structure factor, radial distribution function and momentum distribution of the spin polarized uniform electron gas", G. Ortiz and P. Ballone, *Phys. Rev.* B. 50, 1391 (1994).

"Macroscopic polarization as a geometric quantum phase: many-body formulation", G. Ortiz, and R.M. Martin, *Phys. Rev.* B 49, 14202 (1994).

"New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field", G. Ortiz, D.M. Ceperley, and R.M. Martin, *Phys. Rev. Lett.* 71, 2777 (1993).

"Adiabatic perturbation theory and geometric phases for degenerate systems", G. Rigolin and G. Ortiz, *Phys. Rev. Lett.* 104, 170406 (2010).

"Beyond the quantum adiabatic approximation: adiabatic perturbation theory", G. Rigolin, G. Ortiz, and V. H. Ponce, *Phys. Rev.* A 78, 052508 (2008).

"Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions", S. Deng, G. Ortiz, and L. Viola, *Europhysics Letters* 84, 67008 (2008).

"Quantum approach to classical statistical mechanics", R. Somma, C. D. Batista, and G. Ortiz, *Phys. Rev. Lett.* 99, 030603 (2007).

"Optimal quantum measurements of expectation value of observables", E. Knill, G. Ortiz, and R. Somma, *Phys. Rev.* A 75, 012328 (2007).

"Quantum phase transitions in matrix product systems", M. M. Wolf, G. Ortiz, F. Verstraete, and J. I. Cirac, *Phys. Rev. Lett.* 97, 110403 (2006).

"Liquid state NMR simulations of quantum many-body problems", C. Negreverne, R. Somma, G. Ortiz, E. Knill, and R. Laflamme, *Phys. Rev.* A 71, 032344 (2005).

"A subsystem-independent generalization of entanglement", H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, *Phys. Rev. Lett.* 92, 107902 (2004).

"Tunneling measurement of a single quantum spin", L. Bulaevskii and G. Ortiz, *Phys. Rev. Lett.* 90, 040401 (2003).

"Quantum algorithms for fermionc simulations", G. Ortiz, J.E. Gubernatis, R. Laflamme, and E. Knill, *Phys. Rev.* A 64, 22319 (2001).

Theoretical Division, Los Alamos National Laboratory; Institute for Quantum Computing (Waterloo)

Professor, Physics

- ortizg@indiana.edu
- (812) 855-0367
- Swain West 230
- Office Hours

- Postdoctoral Positions, University of Illinois at Urbana-Champaign; Oppenheimer fellow at LANL
- Ph.D., Swiss Federal Institute of Technology, 1987
- M.S., Instituto Balseiro, Bariloche, 1987

condensed matter physics (theoretical)

A great challenge of theoretical physics is understanding and modeling interacting quantum many-body systems or quantum fields, and accurately predicting properties and functionalities of matter from the fundamental laws of quantum mechanics. My research work is in condensed matter physics and quantum information science.

One of my main interests centers on the physics of strongly coupled systems, which is one of today's most active research areas in condensed matter. These systems happened to be strongly correlated since no obvious small coupling constant exists, and consequently exhibit high sensitivity to small parameter changes. My interest is fueled by the new states of matter such systems can display and the exceptional material properties these phases sometimes exhibit. The physics of high temperature superconducting materials, lanthanide and actinide materials (often referred to as f-electron materials), quantum Hall systems, etc. are cases in point. Indeed, the multiplicity of distinct and novel quantum phases observed experimentally confront us with new paradigms that challenge our understanding of the fundamental principles behind such complex phenomena. For example, whether the mechanism controlling the coexistence and/or competition between magnetism and superconductivity (or Bose-Einstein condensation) has the same physical origin in different classes of materials is still an open question. This complex phenomena exhibited by Nature exceeds our ability to explain them, in part, because of a lack of appropriate mathematical tools to disentangle its mysteries. From the theoretical viewpoint the hurdle is in the presence of non-linear couplings, non-perturbative phenomena, and a panoply of competing quantum orders. As a result, all possible phases of matter and their transitions cannot (even approximately) be described within Landau's framework and new physics concepts such as topological quantum order emerge.

The quest to explore the ultimate limits and principles of quantum physics is out there. Quantum technologies are no longer a theorist's dream. For example, commercial quantum cryptography devices have become available. I am interested in studying foundational, software, and hardware aspects of quantum computation and information. Because of the exciting recent development of new algorithms, such as Shor's factoring and Grover's quantum search, that solve difficult problems on a quantum computer using algorithms that would be impractical on a classical computer, it is easy to overlook the fact that Feynman's original proposal for quantum computers was for the purpose of solving quantum physics problems. Simulation of physical phenomena using quantum devices is one of my areas of research. I am also concerned with topics of potential overlap between my two research disciplines, where feedback from one field may help to resolve significant problems in the other. After all, a quantum computer is a quantum many-body system. What are the concepts from quantum information that one can use to study or predict phenomena in condensed matter physics? Similarly, what concepts can be borrowed from condensed matter to quantify measures of information? These are fundamental open questions. Designing and building a quantum computer or a quantum simulator is a ultimate example of topics that meet the boundaries of both disciplines. Cold atom physics is another.

"Elements of Phase Transitions and Critical Phenomena", H. Nishimori and G. Ortiz (Oxford University Press, Oxford, 2010).

"Superconductivity in strongly repulsive fermions: The role of kinetic-energy frustration", L. Isaev, G. Ortiz, and C. D. Batista, *Phys. Rev. Lett.* (in press).

"Unified approach to quantum and classical dualities", E. Cobanera, G. Ortiz, and Z. Nussinov, *Phys. Rev. Lett.* 104, 020402 (2010).

"Field-induced orbital antiferromagnetism in Mott insulators", K. A. Al-Hassanieh, C. D. Batista, G. Ortiz, and L. N. Boulaevskii, *Phys. Rev. Lett.* 103, 216402 (2009).

"Local physics of magnetization plateaux in the Shastry-Sutherland model", L. Isaev, G. Ortiz, and J. Dukelsky, *Phys. Rev. Lett* 103, 177201 (2009).

"Breached pairing in trapped three-color atomic Fermi gases", B. Errea, J. Dukelsky, and G. Ortiz, *Phys. Rev.* A (Rapid Communications) 79, 051603 (2009).

"Ferrotoroidic moment as a quantum geometric phase", C. D. Batista, G. Ortiz, and A. A. Aligia, *Phys. Rev. Lett.* 101, 077203 (2008).

"A symmetry principle for topological quantum order", Z. Nussinov and G. Ortiz, Ann. *Phys.* (NY) 324, 977 (2009).

"Autocorrelations and thermal fragility of anyonic loops in topologically quantum ordered systems", Z. Nussinov and G. Ortiz, *Phys. Rev.* B 77, 064302 (2008).

"Integrable models for asymmetric Fermi superfluids: Emergence of a new exotic pairing phase", J. Dukelsky, G. Ortiz, S. Rombouts, and van Houcke, *Phys. Rev. Lett.* 96, 180404 (2006).

"BCS-to-BEC crossover from the exact BCS solution", G. Ortiz and J. Dukelsky, *Phys. Rev.* A 72, 043611 (2005).

"Algebraic approach to interacting quantum systems", C.D. Batista and G. Ortiz, *Adv. in Phys.* 53, 1 (2004).

"Unveiling order behind complexity: Ferromagnetism and Bose-Einstein condensation", C.D. Batista, G. Ortiz, and J.E. Gubernatis, *Phys. Rev.* B (Rapid Communications) 65, 180402 (2002).

"Generalized Jordan-Wigner transformations", C.D. Batista and G. Ortiz, *Phys. Rev. Lett.* 86, 1082 (2001).

"Unified description of the resonance peak and incommensuration in high-Tc superconductors", C.D. Batista, G. Ortiz, and A.V. Balatsky, *Phys. Rev.* B 64, 172508 (2001).

"Quantum phase diagram of the t-Jz chain model", C.D. Batista and G. Ortiz, *Phys. Rev. Lett.* 85, 4755 (2000).

"Inhomogeneity-Induced Superconductivity?", J. Eroles, G. Ortiz, A.V. Balatsky, and A.R. Bishop, *Europhys. Lett.* 50, 540 (2000).

"Quantum-mechanical position operator and localization in extended systems", A.A. Aligia and G. Ortiz, *Phys. Rev. Lett.* 82, 2560 (1999).

"Zero temperature phases of the electron gas", G. Ortiz, M. Harris, and P. Ballone, *Phys. Rev. Lett.* 82, 5317 (1999).

"Exchange-correlation hole in polarized insulators: implications for the microscopic functional theory of dielectrics", G. Ortiz, I. Souza, and R.M. Martin, *Phys. Rev. Lett.* 80, 353 (1998).

"Functional theory of extended Coulomb systems", R.M. Martin and G. Ortiz, *Phys. Rev.* B 56, 1124 (1997).

"Correlation energy, structure factor, radial distribution function and momentum distribution of the spin polarized uniform electron gas", G. Ortiz and P. Ballone, *Phys. Rev.* B. 50, 1391 (1994).

"Macroscopic polarization as a geometric quantum phase: many-body formulation", G. Ortiz, and R.M. Martin, *Phys. Rev.* B 49, 14202 (1994).

"New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field", G. Ortiz, D.M. Ceperley, and R.M. Martin, *Phys. Rev. Lett.* 71, 2777 (1993).

"Adiabatic perturbation theory and geometric phases for degenerate systems", G. Rigolin and G. Ortiz, *Phys. Rev. Lett.* 104, 170406 (2010).

"Beyond the quantum adiabatic approximation: adiabatic perturbation theory", G. Rigolin, G. Ortiz, and V. H. Ponce, *Phys. Rev.* A 78, 052508 (2008).

"Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions", S. Deng, G. Ortiz, and L. Viola, *Europhysics Letters* 84, 67008 (2008).

"Quantum approach to classical statistical mechanics", R. Somma, C. D. Batista, and G. Ortiz, *Phys. Rev. Lett.* 99, 030603 (2007).

"Optimal quantum measurements of expectation value of observables", E. Knill, G. Ortiz, and R. Somma, *Phys. Rev.* A 75, 012328 (2007).

"Quantum phase transitions in matrix product systems", M. M. Wolf, G. Ortiz, F. Verstraete, and J. I. Cirac, *Phys. Rev. Lett.* 97, 110403 (2006).

"Liquid state NMR simulations of quantum many-body problems", C. Negreverne, R. Somma, G. Ortiz, E. Knill, and R. Laflamme, *Phys. Rev.* A 71, 032344 (2005).

"A subsystem-independent generalization of entanglement", H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, *Phys. Rev. Lett.* 92, 107902 (2004).

"Tunneling measurement of a single quantum spin", L. Bulaevskii and G. Ortiz, *Phys. Rev. Lett.* 90, 040401 (2003).

"Quantum algorithms for fermionc simulations", G. Ortiz, J.E. Gubernatis, R. Laflamme, and E. Knill, *Phys. Rev.* A 64, 22319 (2001).

Theoretical Division, Los Alamos National Laboratory; Institute for Quantum Computing (Waterloo)

- College of Arts & Sciences
- Department of Physics