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

Tuning the quantum critical crossover in quantum dots

Ganpathy N. Murthy

Bulletin of the American Physical SocietyMar 24, 20050 citations

Magnetotransport in a Model of a Disordered Strange Metal

Aavishkar A. Patel, John McGreevy, Daniel P. Arovas +1 more

Despite much theoretical effort, there is no complete theory of the "strange" metal state of the high temperature superconductors, and its linear-in-temperature T resistivity.Recent experiments showing an unexpected linear-in-field B magnetoresistivity have deepened the puzzle.We propose a simple model of itinerant electrons, interacting via random couplings, with electrons localized on a lattice of "quantum dots" or "islands."This model is solvable in a particular large-N limit and can reproduce observed behavior.The key feature of our model is that the electrons in each quantum dot are described by a Sachdev-Ye-Kitaev model describing electrons without quasiparticle excitations.For a particular choice of the interaction between the itinerant and localized electrons, this model realizes a controlled description of a diffusive marginal-Fermi liquid (MFL) without momentum conservation, which has a linear-in-T resistivity and a T ln T specific heat as T → 0. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite-T crossover to a fully incoherent regime that also has a linear-in-T resistivity.We describe the magnetotransport properties of this model and show that the MFL regime has conductivities that scale as a function of B=T; however, the magnetoresistance saturates at large B. We then consider a macroscopically disordered sample with domains of such MFLs with varying densities of electrons and islands.Using an effective-medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the magnetic field B applied perpendicular to the plane of the sample, at large B. The resistance also scales linearly in T at small B, and as TfðB=TÞ at intermediate B. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates.Despite much theoretical effort, there is no complete theory of the "strange" metal state of the high temperature superconductors, and its linear-in-temperature T resistivity.Recent experiments showing an unexpected linear-in-field B magnetoresistivity have deepened the puzzle.We propose a simple model of itinerant electrons, interacting via random couplings, with electrons localized on a lattice of "quantum dots" or "islands."This model is solvable in a particular large-N limit and can reproduce observed behavior.The key feature of our model is that the electrons in each quantum dot are described by a Sachdev-Ye-Kitaev model describing electrons without quasiparticle excitations.For a particular choice of the interaction between the itinerant and localized electrons, this model realizes a controlled description of a diffusive marginal-Fermi liquid (MFL) without momentum conservation, which has a linear-in-T resistivity and a T ln T specific heat as T → 0. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite-T crossover to a fully incoherent regime that also has a linear-in-T resistivity.We describe the magnetotransport properties of this model and show that the MFL regime has conductivities that scale as a function of B=T; however, the magnetoresistance saturates at large B. We then consider a macroscopically disordered sample with domains of such MFLs with varying densities of electrons and islands.Using an effective-medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the magnetic field B applied perpendicular to the plane of the sample, at large B. The resistance also scales linearly in T at small B, and as TfðB=TÞ at intermediate B. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates.

arXiv:1712.05026Physical Review XMay 22, 2018128 citations

Interacting electrons in silicon quantum interconnects

Anantha S. Rao, Christopher David White, Sean R. Muleady +2 more

Coherent interconnects between gate-defined silicon quantum processing units are essential for scalable quantum computation and long-range entanglement. We argue that one-dimensional electron channels formed in the silicon quantum well of a Si/SiGe heterostructure exhibit strong Coulomb interactions and realize strongly interacting Luttinger liquid physics. At low electron densities, the system enters a Wigner regime characterized by dominant 4kF correlations; increasing the electron density leads to a crossover from the Wigner regime to a Friedel regime with dominant 2kF correlations. We support these results through large-scale density matrix renormalization group (DMRG) simulations of the interacting ground state under both screened and unscreened Coulomb potentials. We propose experimental signatures of the Wigner-Friedel crossover via charge transport and charge sensing in both zero- and high-magnetic field limits. We also analyze the impact of short-range correlated disorder - including random alloy fluctuations and valley splitting variations - and identify that the Wigner-Friedel crossover remains robust until disorder levels of about 400 micro eV. Finally, we show that the Wigner regime enables long-range capacitive coupling between quantum dots across the interconnect, suggesting a route to create long-range entanglement between solid-state qubits. Our results position silicon interconnects as a platform for studying Luttinger liquid physics and for enabling architectures supporting nonlocal quantum error correction and quantum simulation.Coherent interconnects between gate-defined silicon quantum processing units are essential for scalable quantum computation and long-range entanglement. We argue that one-dimensional electron channels formed in the silicon quantum well of a Si/SiGe heterostructure exhibit strong Coulomb interactions and realize strongly interacting Luttinger liquid physics. At low electron densities, the system enters a Wigner regime characterized by dominant 4kF correlations; increasing the electron density leads to a crossover from the Wigner regime to a Friedel regime with dominant 2kF correlations. We support these results through large-scale density matrix renormalization group (DMRG) simulations of the interacting ground state under both screened and unscreened Coulomb potentials. We propose experimental signatures of the Wigner-Friedel crossover via charge transport and charge sensing in both zero- and high-magnetic field limits. We also analyze the impact of short-range correlated disorder - including random alloy fluctuations and valley splitting variations - and identify that the Wigner-Friedel crossover remains robust until disorder levels of about 400 micro eV. Finally, we show that the Wigner regime enables long-range capacitive coupling between quantum dots across the interconnect, suggesting a route to create long-range entanglement between solid-state qubits. Our results position silicon interconnects as a platform for studying Luttinger liquid physics and for enabling architectures supporting nonlocal quantum error correction and quantum simulation.

cond-mat.mes-hallCross-listedarXiv:2601.05306Jan 9, 20260 citations

A configuration interaction analysis of exchange in double quantum dots

Erik Nielsen, Richard P. Muller

We describe in detail a full configuration interaction (CI) method designed to analyze systems of quantum dots. This method is capable of exploring large regions of parameter space, like more approximate approaches such as Heitler London and Hund Mulliken, though it is not limited to weakly coupled dots. In particular, this method is well-suited to the analysis of solid state quantum-dot-based qubits, and we consider the case of a double quantum dot (DQD) singlet-triplet qubit. Past analyses have used techniques which are either substantially restricted in the regimes they can be used, or device specific and unsuited to exploration of a large regions of parameter space. We analyze how the DQD exchange energy, which is central to the operation of qubit rotation gates, depends on a generic set of system parameters including magnetic field, DQD detuning, dot size, and dot separation. We discuss the implications of these results to the construction of real devices. We provide a benchmark of the CI by directly comparing results from the CI method with exact results for two electrons in a single parabolic potential (dot).We describe in detail a full configuration interaction (CI) method designed to analyze systems of quantum dots. This method is capable of exploring large regions of parameter space, like more approximate approaches such as Heitler London and Hund Mulliken, though it is not limited to weakly coupled dots. In particular, this method is well-suited to the analysis of solid state quantum-dot-based qubits, and we consider the case of a double quantum dot (DQD) singlet-triplet qubit. Past analyses have used techniques which are either substantially restricted in the regimes they can be used, or device specific and unsuited to exploration of a large regions of parameter space. We analyze how the DQD exchange energy, which is central to the operation of qubit rotation gates, depends on a generic set of system parameters including magnetic field, DQD detuning, dot size, and dot separation. We discuss the implications of these results to the construction of real devices. We provide a benchmark of the CI by directly comparing results from the CI method with exact results for two electrons in a single parabolic potential (dot).

arXiv:1006.2735Physical Review BJun 14, 20103 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.