Quantum dots with a large Thouless number $g$ embody a regime where both disorder and interactions can be treated nonperturbatively using large- $N$ techniques (with $N=g$ ) and quantum phase transitions can be studied. Here we focus on dots where the noninteracting Hamiltonian is drawn from a crossover ensemble between two symmetry classes, where the crossover parameter introduces a tunable energy scale independent of and much smaller than the Thouless energy. We show that the quantum critical regime, dominated by collective critical fluctuations, can be accessed at this energy scale. The nonperturbative physics of this regime can only be described by the large- $N$ approach, as we illustrate with two experimentally relevant examples.Quantum dots with a large Thouless number $g$ embody a regime where both disorder and interactions can be treated nonperturbatively using large-$N$ techniques (with $N=g$) and quantum phase transitions can be studied. Here we focus on dots where the noninteracting Hamiltonian is drawn from a crossover ensemble between two symmetry classes, where the crossover parameter introduces a tunable energy scale independent of and much smaller than the Thouless energy. We show that the quantum critical regime, dominated by collective critical fluctuations, can be accessed at this energy scale. The nonperturbative physics of this regime can only be described by the large-$N$ approach, as we illustrate with two experimentally relevant examples.

arXiv:cond-mat/0406029Physical Review BOct 15, 200410 citations

Interacting electrons in a quantum dot : quantum Monte Carlo studies

Ari Harju

Jan 1, 19990 citations

Universal interacting crossover regime in two-dimensional quantum dots

Ganpathy N. Murthy

Interacting electrons in quantum dots with large Thouless number $g$ in the three classical random matrix symmetry classes are well understood. When a specific type of spin-orbit coupling known to be dominant in two-dimensional semiconductor quantum dots is introduced, we show that an interacting quantum critical crossover energy scale emerges and low-energy quasiparticles generically have a decay width proportional to their energy. The low-energy physics of this system is an example of a universal interacting crossover regime.Interacting electrons in quantum dots with large Thouless number $g$ in the three classical random matrix symmetry classes are well understood. When a specific type of spin-orbit coupling known to be dominant in two-dimensional semiconductor quantum dots is introduced, we show that an interacting quantum critical crossover energy scale emerges and low-energy quasiparticles generically have a decay width proportional to their energy. The low-energy physics of this system is an example of a universal interacting crossover regime.

arXiv:0706.3406Physical Review BFeb 21, 20087 citations

Quantum criticality near the Stoner transition in a system of two tunnel-coupled quantum dots with spin-orbit coupling

Oleksandr Zelyak, Ganpathy N. Murthy

We study a system of two tunnel-coupled quantum dots with the first dot containing interacting electrons (described by the universal Hamiltonian) not subject to spin-orbit coupling whereas the second contains noninteracting electrons subject to spin-orbit coupling. We focus on describing the behavior of the system near the Stoner transition. Close to the critical point quantum fluctuations become important and the system enters a quantum-critical regime. The large- $N$ approximation allows us to calculate physical quantities reliably even in this strongly fluctuating regime. In particular, we find a scaling function to describe the crossover of the quasiparticle decay rate between the renormalized Fermi-liquid regime and the quantum-critical regime.We study a system of two tunnel-coupled quantum dots with the first dot containing interacting electrons (described by the universal Hamiltonian) not subject to spin-orbit coupling whereas the second contains noninteracting electrons subject to spin-orbit coupling. We focus on describing the behavior of the system near the Stoner transition. Close to the critical point quantum fluctuations become important and the system enters a quantum-critical regime. The large-$N$ approximation allows us to calculate physical quantities reliably even in this strongly fluctuating regime. In particular, we find a scaling function to describe the crossover of the quasiparticle decay rate between the renormalized Fermi-liquid regime and the quantum-critical regime.

arXiv:0906.1838Physical Review BNov 12, 20097 citations

Quantum dots with a large Thouless number

g

embody a regime where both disorder and interactions can be treated nonperturbatively using large-

N

techniques (with

N=g

) and quantum phase transitions can be studied. Here we focus on dots where the noninteracting Hamiltonian is drawn from a crossover ensemble between two symmetry classes, where the crossover parameter introduces a tunable energy scale independent of and much smaller than the Thouless energy. We show that the quantum critical regime, dominated by collective critical fluctuations, can be accessed at this energy scale. The nonperturbative physics of this regime can only be described by the large-

N

approach, as we illustrate with two experimentally relevant examples.

Interacting electrons in quantum dots with large Thouless number

g

in the three classical random matrix symmetry classes are well understood. When a specific type of spin-orbit coupling known to be dominant in two-dimensional semiconductor quantum dots is introduced, we show that an interacting quantum critical crossover energy scale emerges and low-energy quasiparticles generically have a decay width proportional to their energy. The low-energy physics of this system is an example of a universal interacting crossover regime.

N

approximation allows us to calculate physical quantities reliably even in this strongly fluctuating regime. In particular, we find a scaling function to describe the crossover of the quasiparticle decay rate between the renormalized Fermi-liquid regime and the quantum-critical regime.