Local wave-packet spectroscopy of the Drude weight in Tomonaga-Luttinger liquids

summary

Video file (mp4)

The gist

The gist The local pulse electric field creates two counterpropagating packets with opposite accumulated charges ±qK and velocity v, where K and v are the TLL parameter and velocity, allowing the

In short

The study investigates how a local electric pulse in a Tomonaga-Luttinger liquid (TLL) generates counterpropagating charge packets with opposite charges. These packets cause a linearly growing charge polarization, allowing researchers to extract the Drude weight, D=vK, from real-time dynamics. This confirms that the Drude weight governs both uniform current response and the ballistic motion of locally created charge packets.

Key concepts

Tomonaga-Luttinger liquid (TLL)
A one-dimensional quantum system where interacting fermions behave like collective excitations rather than individual particles. It is described by a low-energy Hamiltonian that governs how charge and spin move in this specific quantum fluid state.
Bosonization
A mathematical technique used to describe the low-energy physics of 1D interacting systems, mapping fermionic degrees of freedom onto simpler bosonic fields. This allows for the calculation of collective excitations like charge density waves and currents.
Drude weight (D=vK)
A fundamental parameter in TLLs that quantifies the system's response to a uniform electric field, representing the stiffness or inertia related to charge transport. The paper shows this weight is also responsible for driving the real-time motion of locally generated charge packets.
Charge Polarization (P(t))
A measure of how much charge is separated or accumulated in space and time due to a non-equilibrium field. In this study, P(t) grows linearly with time as 2qDt, directly linking the system's response to the packet dynamics.

Terminology used across episodes

This episode discusses

The paper

Local wave-packet spectroscopy of the Drude weight in Tomonaga-Luttinger liquids · Read on arXiv

Takayuki Yokoyama, *, Yasuhiro Tada

Quantum Matter Program, Graduate School of Advanced Science and Engineering, Hiroshima University · Institute for Solid State Physics, University of Tokyo

We investigate wave packets generated by a local pulse electric field in a Tomonaga-Luttinger liquid (TLL) with a U(1) charge q. Bosonization shows that a local pulse field creates two counterpropagating packets with opposite accumulated charges plus or minus qK and velocity v, where K and v are the TLL parameter and velocity. The packet motion produces a linearly growing charge polarization P(t)=2 qDt in the conducting TLL at non-equilibrium, allowing the Drude weight D=vK to be extracted from real-time local dynamics. We test this local-packet description by time-dependent variational principle simulations of the spin-1/2 XXZ chain. The simulations visualize the density, current, energy, and entanglement profiles in the space-time plane and confirm the predicted packet charge and propagation velocity. We also show that excess energy and entanglement remaining near the pulse region are suppressed in the weak-pulse limit. Finally, the Drude weight obtained from the packet-induced polarization agrees with the exact Bethe-ansatz result, demonstrating local-packet spectroscopy of intrinsic transport in a TLL.

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: Today's paper: "Local wave-packet spectroscopy of the Drude weight in Tomonaga-Luttinger liquids".

Mira: The gist The local pulse electric field creates two counterpropagating packets with opposite accumulated charges ±qK and velocity v, where K and v are the TLL parameter and velocity,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: Okay, so we're diving into the details of "Local wave-packet spectroscopy of the Drude weight in Tomonaga-Luttinger liquids." The paper starts by setting up a system with a conserved U(one) charge, like the spin-one/two XXZ chain, and applying a local pulse electric field or equivalently a U(one) twist <ref:2610.22257#pg1,the spin-1/2 XXZ chain>.

Mira: They use bosonization for this TLL fixed point Hamiltonian HTLL = v squared over two pi Z dx K of the partial derivative theta squared plus one over K of the partial derivative phi squared <ref:2610.22257#pg1>. And they explain that this setup is different from voltage pulse protocols because it applies a spatially extended but temporally impulsive field directly to the bulk.

Lev: The low-energy Hamiltonian involves excitation velocity v and the TLL parameter K, where K is related to the stiffness of the system according to reference eight <ref:2610.22257#pg2>. They define canonical conjugate fields phi and theta that satisfy this relationship for their U(one) charge sector <ref:2610.22257#pg1>.

Kai: Just before the pulse, they look at the current density being zero at t equals zero minus, jx over x equals q v K pi partial x theta minus phi at t equals zero minus, which is standard ground state behavior.

Mira: Immediately after the instantaneous quench, because the quantum state doesn't change instantly, they find that the current density becomes jx over x equals q v K pi partial x theta at t equals zero plus. This sets up the dynamics for what happens next.

Lev: The dynamics of the theta field are then described by chiral fields phi R at x minus vt equal K theta of x t minus phi and phi L at x plus vt equal K theta of x t plus phi. These are the right-moving and left-moving components.

Kai: From these chiral fields, they decompose the current density into two components, rho R and rho L, which are related to partial derivatives of these chiral fields scaled by over two pi.

Mira: The resulting current density at time t greater than zero is given by the expression q v K over two pi partial x theta of x minus vt plus partial x theta of x plus vt. This describes the motion after the pulse hits.

Lev: They then define an excess charge density delta rho, which is related to the sum of these right- and left-moving components, given by q K over two pi partial x theta of x minus vt minus partial x theta of x plus vt.

Kai: When they consider a specific electric field profile E(x) that looks like one over two pi times one at zero, they get a packet width W equal to l and a height h equal to q K over l.

Mira: The key finding is that for time t greater than l over v, the right-moving packet has charge Q right equal plus q K and the left-moving packet has charge Q left equal minus q K.

Lev: This leads them to define the charge polarization P(t) as Z dx x delta rho of x t, which they rewrite as two times v t times Q right minus two times v t times Q left.

Kai: And this simplifies beautifully to P(t) equal two q D t where D is the Drude weight, which is defined as v K. This allows them to extract D from real-time local dynamics.

Conclusion: Mira: So, wrapping up the paper "Local wave-packet spectroscopy of the Drude weight in Tomonaga-Luttinger liquids," it really shows how you can use a local electric field pulse as a probe for intrinsic transport properties.

Kai: The main message is that this local pulse creates two counterpropagating packets with opposite accumulated U(one) charges, plus qK and minus qK, propagating at velocity v <ref:2610.22257#pg1,creates two counterpropagating packets with opposite accumulated>.

Lev: These packets cause the charge polarization to grow linearly in time as P of t equals two q D t, where D is the Drude weight equal to v K. This confirms that the local-packet protocol provides a real-space way to probe this intrinsic Drude weight in a lattice TLL.

Mira: It shows that the same stiffness governing uniform current response also controls the dipole motion of these locally generated charge packets, and they confirm this by matching their result to the exact Bethe ansatz result.

Kai: The authors are Takayuki Yokoyama and Yasuhiro Tada, and what this means is that we now have a way to spectroscopically measure transport in TLLs using local dynamics rather than just uniform current measurements.

Lev: It suggests that the Drude weight isn't just a coefficient for how much charge you move uniformly, but it governs the real-time motion of locally generated charge packets in a TLL.

Mira: So, this work opens up new ways to look at transport by linking real-space local measurements to bulk properties of these one-dimensional systems.

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