x1 y1 y2 x2 b2 b1 y1 x1 x1 y2 y2 x2 x2 y1 - Nature

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Supplementary Information. Arvind Murugan and Suriyanarayanan Vaikuntanathan∗. The University of Chicago, Chicago, IL, 60637 x1 y1 y2 x2 b1 b2 b2 b1 y1.
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=

Supplementary Information Arvind Murugan and Suriyanarayanan Vaikuntanathan∗ The University of Chicago, Chicago, IL, 60637

f2i+3

f2i+1

f2i

x2

x2

x2

y2

y2

y2

b1 b2

LLeft

Interface

b1 b2

y1

y1

y1

x1

x1

x1 f2i

f2i+2

1

f2i

2

SUPPLEMENTARY FIG 1. Toy network introduced in the main text with one boundary. In this case, the right network WR is simply vacuum. We are interested in conditions under this network can support a localized edge mode at the right edge (blue highlighted curve).

0.25

e(λ)

Eigenvalue

0.20

e2 (λ)

0.15 0.10 0.05 0.00 -0.05 -0.4

-0.2

0.0 λ

0.2

0.4

SUPPLEMENTARY FIG 2. The first two eigenvalues of W (λ). We have plotted the real part of the second eigenvalue. The parameters are the same as those in Fig 2. As in the main text, we simulated a system in which two bulk networks L and R are connected by interfaces. The number of vertical rungs in the network is N = 200.

2

A) λ