🔬 condensed matter

Spinless charged excitation at the interface between a conventional topological insulator and a topological Mott insulator

Using extensive density-matrix renormalization group calculations on the triangular-lattice Hofstadter-Hubbard model, this study reveals that the interface between an integer quantum Hall state and a chiral spin liquid hosts a unique spinless charged excitation, while also characterizing fractionalization in the bulk chiral spin liquid and spin-triplet exciton formation in the integer quantum Hall phase.

Original authors: Cesar A. Gallegos, Andrew J. Millis, Steven R. White

Published 2026-07-17

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CC BY 4.0

Original authors: Cesar A. Gallegos, Andrew J. Millis, Steven R. White

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world of materials not just as solid blocks of stuff, but as landscapes with hidden rules. In the strange realm of quantum physics, some materials are "insulators," meaning they usually block electricity. But there's a special class called "topological insulators." Think of these like a chocolate bar with a hard, insulating shell but a gooey, conductive center that only flows along the very edges. If you cut one open, the edge becomes a superhighway for electrons, carrying both their electric charge and their tiny internal magnetism (spin).

Now, imagine a different kind of exotic material called a "topological Mott insulator." Here, the electrons are so crowded and grumpy with each other that they break apart. Instead of moving as whole particles, they split into two separate ghosts: one ghost carries the electric charge but has no spin, and the other carries the spin but has no charge. This is called "fractionalization." Scientists are fascinated by what happens when you smash these two different worlds together. If you build a wall between a normal topological insulator and this split-ghost material, what kind of weird highway appears at the boundary? Does it carry both charge and spin? Does it carry neither? Or does it create something entirely new? Understanding these boundaries helps physicists design future quantum computers and materials that can do things we can't even imagine yet.

This paper dives into that exact question, simulating a meeting point between an "Integer Quantum Hall" state (our chocolate-bar insulator) and a "Chiral Spin Liquid" (the split-ghost material). The researchers, using powerful computer calculations on a model of a triangular grid of atoms, discovered a truly bizarre phenomenon at the interface. They found that the boundary hosts a "spinless charged excitation." To use a playful metaphor: imagine a parade where the marchers usually carry both a heavy backpack (charge) and a spinning top (spin). At this specific interface, the backpacks detach from the tops. The backpacks get stuck right at the border, marching in place, while the spinning tops are kicked away into the crowd. The result is a mode that carries electricity but has absolutely no magnetic spin attached to it.

The team didn't just guess this; they simulated the system on a "cylinder" of atoms and watched what happened when they twisted magnetic fields through it. When they pumped electric charge into the system, it flowed from one side and stopped dead at the interface, piling up there. However, when they pumped spin, it flowed right through the interface, ignoring the boundary entirely and exiting the other side. This confirmed that the interface acts like a one-way street for charge but a free pass for spin.

Furthermore, the paper looked at what happens when you try to create a single electron near this border. In the "split-ghost" part of the material, the electron naturally falls apart into its charge and spin components. But at the interface, the charge component gets trapped tightly to the wall, while the spin component is repelled and floats away into the bulk material. This suggests the interface supports a unique "edge state" that allows charge to exist without spin.

The researchers also checked the "bulk" (the middle) of both materials. In the split-ghost material, they saw the expected fractionalization: a single electron splits into a charge carrier and a spin carrier that drift apart. In the normal insulator, electrons stay whole, but they can form "excitons"—pairs of an electron and a "hole" (a missing electron) that stick together like a magnet, creating a low-energy spin wave. Interestingly, this sticking together gets weaker as the material gets closer to the point where it transforms into the split-ghost state, but the simulations suggest it doesn't vanish completely right at the transition.

In short, the paper suggests that by engineering the boundary between these two exotic phases, nature creates a new kind of particle-like behavior: a charge that is completely divorced from its spin. While these results come from high-precision computer simulations rather than a physical lab experiment, the evidence within the model is strong and consistent, pointing toward a fascinating new way to control electricity in future quantum devices.

Technical Summary: Spinless Charged Excitation at the IQH–CSL Interface

Problem Statement
The paper investigates the nature of excitations at the interface separating two topologically distinct insulating phases: the Integer Quantum Hall (IQH) state and the Chiral Spin Liquid (CSL). While boundaries between topological phases and vacuum are known to host gapless edge modes determined by the change in wavefunction topology, the behavior at an interface between two distinct topological bulk phases is less understood. Specifically, the authors address the theoretical proposal that an interface between a Topological Insulator (TI) and a Topological Mott Insulator (TMI) might reconstruct such that the spin sector becomes gapped while the charge sector remains gapless, resulting in a propagating "spinless charged" mode. The study focuses on realizing this scenario in the triangular-lattice Hofstadter-Hubbard model, where the IQH phase (a TI analog) and the CSL phase (a TMI analog) can be stabilized by tuning the Hubbard interaction strength.

Methodology
The authors employ extensive Density Matrix Renormalization Group (DMRG) calculations on finite-radius cylinders with periodic boundary conditions in the transverse direction and open boundaries in the longitudinal direction.

Model: The system is defined by the triangular-lattice Hofstadter-Hubbard Hamiltonian with complex hoppings encoding a $\pi/2$ flux per triangle. The study focuses on the half-filled ground state with zero Zeeman coupling.
Interface Construction: To create the IQH–CSL interface, the Hubbard interaction $U$ is made spatially dependent. The left region of the cylinder is set to $U=8$ (within the IQH phase, $U < U_c$ ), and the right region to $U=14$ (within the CSL phase, $U > U_c$ ), with the transition occurring across a single bond.
Probes:
1. Flux Insertion (Pumping): The authors adiabatically thread magnetic flux $\Phi$ through the cylinder axis. They analyze the response to charge pumping (flux of same sign for both spins) and spin pumping (flux of opposite signs for up/down spins) to track the transport of charge and spin density.
2. Excited State Calculations: Trial states are constructed by adding/removing electrons or creating spin flips (magnons) in the bulk and near the interface. These states are relaxed using DMRG to approximate eigenstates, allowing for the visualization of charge density ( $n$ ) and magnetization ( $S^z$ ) profiles.
Parameters: Calculations were performed on cylinders with transverse periodicities of 3, 5, and 6 (labeled YC3, YC5, YC6), utilizing bond dimensions up to $\chi=6000$ for pumping and $\chi=1500$ for excited states, achieving truncation errors of $O(10^{-5})$ to $O(10^{-6})$ .

Key Results

Interface Excitations (Spinless Charged Mode):
- Flux Pumping: Under charge pumping, charge is removed from the IQH-vacuum edge and accumulates at the IQH–CSL interface, indicating the interface supports a charge mode. Conversely, under spin pumping, spin density is transferred from the IQH-vacuum edge directly to the CSL-vacuum edge, passing through the interface with negligible accumulation. This demonstrates that the interface traps charge but allows spin to pass, consistent with a spinless charged mode.
- Single-Particle Excitations: When an electron is added near the interface, the excitation fractionalizes. The charge component (chargon) remains tightly bound to the interface, while the spin component (spinon) is expelled into the CSL bulk. The interaction between the spinon and the interface is repulsive.
- Spin-Triplet Excitations: Charge-neutral spin-triplet excitations at the interface separate into two spatially separated spinons located on the CSL side of the interface, further confirming the absence of spin binding to the interface.
Bulk Excitations:
- CSL Phase: The bulk CSL exhibits strong fractionalization. Single-particle excitations separate into a chargon and a spinon. Charge-neutral spin-triplet excitations split into two spatially separated spinons, each carrying $S^z = 1/2$ .
- IQH Phase: Single-particle excitations behave as electrons with bound charge and spin. Charge-neutral spin-triplet excitations form bound electron-hole pairs (spin-triplet excitons). The binding energy of these excitons scales quadratically with $U$ at small interactions but decreases near the critical interaction $U_c$ .

Significance and Claims
The paper claims to provide strong numerical evidence that the interface between an Integer Quantum Hall state and a Chiral Spin Liquid hosts a unique gapless excitation: a spinless charged mode. This mode is characterized by a charge component (chargon) tightly bound to the interface and a spin component that is repelled into the bulk.

The authors identify this state through two complementary methods:

Topological Response: Flux insertion shows that charge pumps halt at the interface while spin pumps traverse it, directly demonstrating the decoupling of charge and spin transport at the boundary.
Spectral Analysis: Direct calculation of low-lying excited states confirms that single-particle excitations fractionalize at the interface, with the charge sector localized and the spin sector delocalized.

The work validates the theoretical proposal that interfaces between distinct topological phases can reconstruct to support exotic edge states that differ fundamentally from the edge modes of either constituent bulk phase. The authors also note that the small but non-zero spin gap near the IQH-CSL transition point warrants further investigation regarding the nature of phases occurring near this critical point.

Technical Summary: Spinless Charged Excitation at the IQH–CSL Interface

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